LMFDB - Embedded newform 546.2.by.a.115.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.8
Character	$\chi$	$=$	546.115
Dual form			546.2.by.a.19.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(2.30819 + 0.618478i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(1.78879 + 1.94942i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(2.30819 + 0.618478i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(1.78879 + 1.94942i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +2.38962 q^{10} +(-1.45718 + 1.45718i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(3.60510 + 0.0570287i) q^{13} +(2.23239 + 1.42002i) q^{14} +(0.618478 - 2.30819i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.37950 - 2.38937i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(-4.53108 + 4.53108i) q^{19} +(2.30819 - 0.618478i) q^{20} +(1.94942 - 1.78879i) q^{21} +(-1.03038 + 1.78467i) q^{22} +(2.12942 + 1.22942i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(0.615104 + 0.355130i) q^{25} +(3.49702 - 0.877983i) q^{26} +1.00000i q^{27} +(2.52385 + 0.793847i) q^{28} +(-1.69638 - 2.93821i) q^{29} -2.38962i q^{30} +(-1.60157 - 5.97714i) q^{31} +(0.258819 - 0.965926i) q^{32} +(1.45718 + 1.45718i) q^{33} +(-1.95091 - 1.95091i) q^{34} +(2.92320 + 5.60595i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-2.80883 - 10.4827i) q^{37} +(-3.20396 + 5.54942i) q^{38} +(0.0570287 - 3.60510i) q^{39} +(2.06947 - 1.19481i) q^{40} +(-9.91867 - 2.65770i) q^{41} +(1.42002 - 2.23239i) q^{42} +(6.84806 + 3.95373i) q^{43} +(-0.533364 + 1.99054i) q^{44} +(-2.30819 - 0.618478i) q^{45} +(2.37506 + 0.636396i) q^{46} +(-0.0569467 + 0.212528i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-0.600442 + 6.97420i) q^{49} +(0.686059 + 0.183829i) q^{50} +(-2.38937 + 1.37950i) q^{51} +(3.15062 - 1.75316i) q^{52} +(3.80074 - 6.58307i) q^{53} +(0.258819 + 0.965926i) q^{54} +(-4.26468 + 2.46221i) q^{55} +(2.64331 + 0.113578i) q^{56} +(4.53108 + 4.53108i) q^{57} +(-2.39904 - 2.39904i) q^{58} +(2.48940 - 9.29055i) q^{59} +(-0.618478 - 2.30819i) q^{60} +8.92123i q^{61} +(-3.09399 - 5.35896i) q^{62} +(-1.78879 - 1.94942i) q^{63} -1.00000i q^{64} +(8.28599 + 2.36131i) q^{65} +(1.78467 + 1.03038i) q^{66} +(4.57970 + 4.57970i) q^{67} +(-2.38937 - 1.37950i) q^{68} +(1.22942 - 2.12942i) q^{69} +(4.27453 + 4.65835i) q^{70} +(-5.69654 + 1.52638i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(-11.7734 + 3.15468i) q^{73} +(-5.42625 - 9.39854i) q^{74} +(0.355130 - 0.615104i) q^{75} +(-1.65849 + 6.18957i) q^{76} +(-5.44724 - 0.234056i) q^{77} +(-0.877983 - 3.49702i) q^{78} +(3.79955 + 6.58102i) q^{79} +(1.68971 - 1.68971i) q^{80} +1.00000 q^{81} -10.2686 q^{82} +(-9.18598 + 9.18598i) q^{83} +(0.793847 - 2.52385i) q^{84} +(-1.70639 - 6.36832i) q^{85} +(7.63802 + 2.04660i) q^{86} +(-2.93821 + 1.69638i) q^{87} +2.06076i q^{88} +(0.410929 - 0.110108i) q^{89} -2.38962 q^{90} +(6.33760 + 7.12985i) q^{91} +2.45885 q^{92} +(-5.97714 + 1.60157i) q^{93} +0.220025i q^{94} +(-13.2610 + 7.65623i) q^{95} +(-0.965926 - 0.258819i) q^{96} +(1.25085 + 4.66823i) q^{97} +(1.22507 + 6.89197i) q^{98} +(1.45718 - 1.45718i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) $ 32 * q + 8 * q^7 - 32 * q^9	$ 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	2.30819	+	0.618478i	1.03225	+	0.276592i	0.734900	−	0.678175i	$-0.237229\pi$
$5$	2.30819	+	0.618478i	1.03225	+	0.276592i	0.297354	+	0.954767i	$0.403896\pi$
$6$	−0.258819	−	0.965926i	−0.105662	−	0.394338i
$7$	1.78879	+	1.94942i	0.676100	+	0.736810i
$7$	1.78879	+	1.94942i	0.676100	+	0.736810i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	2.38962			0.755663
$11$	−1.45718	+	1.45718i	−0.439356	+	0.439356i	−0.891795	−	0.452439i	$-0.850554\pi$
$11$	−1.45718	+	1.45718i	−0.439356	+	0.439356i	0.452439	+	0.891795i	$0.350554\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	3.60510	+	0.0570287i	0.999875	+	0.0158169i
$13$	3.60510	+	0.0570287i	0.999875	+	0.0158169i
$14$	2.23239	+	1.42002i	0.596630	+	0.379516i
$15$	0.618478	−	2.30819i	0.159690	−	0.595972i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.37950	−	2.38937i	−0.334579	−	0.579508i	0.648825	−	0.760938i	$-0.275261\pi$
$17$	−1.37950	−	2.38937i	−0.334579	−	0.579508i	−0.983404	+	0.181430i	$0.941927\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	−4.53108	+	4.53108i	−1.03950	+	1.03950i	−0.0403146	+	0.999187i	$0.512836\pi$
$19$	−4.53108	+	4.53108i	−1.03950	+	1.03950i	−0.999187	+	0.0403146i	$0.987164\pi$
$20$	2.30819	−	0.618478i	0.516127	−	0.138296i
$21$	1.94942	−	1.78879i	0.425397	−	0.390347i
$22$	−1.03038	+	1.78467i	−0.219678	+	0.380493i
$23$	2.12942	+	1.22942i	0.444015	+	0.256352i	0.705299	−	0.708910i	$-0.250813\pi$
$23$	2.12942	+	1.22942i	0.444015	+	0.256352i	−0.261284	+	0.965262i	$0.584146\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	0.615104	+	0.355130i	0.123021	+	0.0710261i
$26$	3.49702	−	0.877983i	0.685822	−	0.172187i
$27$			1.00000i			0.192450i
$28$	2.52385	+	0.793847i	0.476962	+	0.150023i
$29$	−1.69638	−	2.93821i	−0.315009	−	0.545612i	0.664430	−	0.747350i	$-0.268674\pi$
$29$	−1.69638	−	2.93821i	−0.315009	−	0.545612i	−0.979439	+	0.201739i	$0.935341\pi$
$30$		−	2.38962i		−	0.436282i
$31$	−1.60157	−	5.97714i	−0.287650	−	1.07353i	−0.946881	−	0.321585i	$-0.895784\pi$
$31$	−1.60157	−	5.97714i	−0.287650	−	1.07353i	0.659230	−	0.751941i	$-0.270882\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	1.45718	+	1.45718i	0.253662	+	0.253662i
$34$	−1.95091	−	1.95091i	−0.334579	−	0.334579i
$35$	2.92320	+	5.60595i	0.494112	+	0.947579i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	−2.80883	−	10.4827i	−0.461769	−	1.72335i	−0.667384	−	0.744714i	$-0.732586\pi$
$37$	−2.80883	−	10.4827i	−0.461769	−	1.72335i	0.205615	−	0.978633i	$-0.434081\pi$
$38$	−3.20396	+	5.54942i	−0.519751	+	0.900235i
$39$	0.0570287	−	3.60510i	0.00913191	−	0.577278i
$40$	2.06947	−	1.19481i	0.327212	−	0.188916i
$41$	−9.91867	−	2.65770i	−1.54904	−	0.415063i	−0.619863	−	0.784710i	$-0.712812\pi$
$41$	−9.91867	−	2.65770i	−1.54904	−	0.415063i	−0.929172	+	0.369647i	$0.879479\pi$
$42$	1.42002	−	2.23239i	0.219113	−	0.344465i
$43$	6.84806	+	3.95373i	1.04432	+	0.602938i	0.921054	−	0.389436i	$-0.127330\pi$
$43$	6.84806	+	3.95373i	1.04432	+	0.602938i	0.123266	+	0.992374i	$0.460663\pi$
$44$	−0.533364	+	1.99054i	−0.0804077	+	0.300086i
$45$	−2.30819	−	0.618478i	−0.344085	−	0.0921972i
$46$	2.37506	+	0.636396i	0.350184	+	0.0938315i
$47$	−0.0569467	+	0.212528i	−0.00830654	+	0.0310004i	−0.969955	−	0.243286i	$-0.921775\pi$
$47$	−0.0569467	+	0.212528i	−0.00830654	+	0.0310004i	0.961648	+	0.274286i	$0.0884415\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−0.600442	+	6.97420i	−0.0857775	+	0.996314i
$50$	0.686059	+	0.183829i	0.0970234	+	0.0259974i
$51$	−2.38937	+	1.37950i	−0.334579	+	0.193169i
$52$	3.15062	−	1.75316i	0.436913	−	0.243120i
$53$	3.80074	−	6.58307i	0.522071	−	0.904254i	−0.477599	−	0.878578i	$-0.658493\pi$
$53$	3.80074	−	6.58307i	0.522071	−	0.904254i	0.999670	−	0.0256759i	$-0.00817378\pi$
$54$	0.258819	+	0.965926i	0.0352208	+	0.131446i
$55$	−4.26468	+	2.46221i	−0.575049	+	0.332005i
$56$	2.64331	+	0.113578i	0.353227	+	0.0151774i
$57$	4.53108	+	4.53108i	0.600157	+	0.600157i
$58$	−2.39904	−	2.39904i	−0.315009	−	0.315009i
$59$	2.48940	−	9.29055i	0.324092	−	1.20953i	−0.591130	−	0.806576i	$-0.701318\pi$
$59$	2.48940	−	9.29055i	0.324092	−	1.20953i	0.915222	−	0.402950i	$-0.132015\pi$
$60$	−0.618478	−	2.30819i	−0.0798452	−	0.297986i
$61$			8.92123i			1.14225i	0.820864	+	0.571123i	$0.193492\pi$
$61$			8.92123i			1.14225i	−0.820864	+	0.571123i	$0.806508\pi$
$62$	−3.09399	−	5.35896i	−0.392938	−	0.680588i
$63$	−1.78879	−	1.94942i	−0.225367	−	0.245603i
$64$		−	1.00000i		−	0.125000i
$65$	8.28599	+	2.36131i	1.02775	+	0.292884i
$66$	1.78467	+	1.03038i	0.219678	+	0.126831i
$67$	4.57970	+	4.57970i	0.559499	+	0.559499i	0.929165	−	0.369666i	$-0.120528\pi$
$67$	4.57970	+	4.57970i	0.559499	+	0.559499i	−0.369666	+	0.929165i	$0.620528\pi$
$68$	−2.38937	−	1.37950i	−0.289754	−	0.167290i
$69$	1.22942	−	2.12942i	0.148005	−	0.256352i
$70$	4.27453	+	4.65835i	0.510904	+	0.556780i
$71$	−5.69654	+	1.52638i	−0.676055	+	0.181148i	−0.580481	−	0.814274i	$-0.697135\pi$
$71$	−5.69654	+	1.52638i	−0.676055	+	0.181148i	−0.0955744	+	0.995422i	$0.530469\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	−11.7734	+	3.15468i	−1.37798	+	0.369228i	−0.870386	−	0.492370i	$-0.836131\pi$
$73$	−11.7734	+	3.15468i	−1.37798	+	0.369228i	−0.507591	+	0.861598i	$0.669464\pi$
$74$	−5.42625	−	9.39854i	−0.630789	−	1.09256i
$75$	0.355130	−	0.615104i	0.0410069	−	0.0710261i
$76$	−1.65849	+	6.18957i	−0.190242	+	0.709993i
$77$	−5.44724	−	0.234056i	−0.620770	−	0.0266732i
$78$	−0.877983	−	3.49702i	−0.0994120	−	0.395959i
$79$	3.79955	+	6.58102i	0.427483	+	0.740423i	0.996649	−	0.0818003i	$-0.0260670\pi$
$79$	3.79955	+	6.58102i	0.427483	+	0.740423i	−0.569165	+	0.822223i	$0.692734\pi$
$80$	1.68971	−	1.68971i	0.188916	−	0.188916i
$81$	1.00000			0.111111
$82$	−10.2686			−1.13397
$83$	−9.18598	+	9.18598i	−1.00829	+	1.00829i	−0.00832739	+	0.999965i	$0.502651\pi$
$83$	−9.18598	+	9.18598i	−1.00829	+	1.00829i	−0.999965	+	0.00832739i	$0.997349\pi$
$84$	0.793847	−	2.52385i	0.0866158	−	0.275374i
$85$	−1.70639	−	6.36832i	−0.185084	−	0.690741i
$86$	7.63802	+	2.04660i	0.823629	+	0.220691i
$87$	−2.93821	+	1.69638i	−0.315009	+	0.181871i
$88$			2.06076i			0.219678i
$89$	0.410929	−	0.110108i	0.0435584	−	0.0116714i	−0.236974	−	0.971516i	$-0.576156\pi$
$89$	0.410929	−	0.110108i	0.0435584	−	0.0116714i	0.280532	+	0.959845i	$0.409489\pi$
$90$	−2.38962			−0.251888
$91$	6.33760	+	7.12985i	0.664361	+	0.747411i
$92$	2.45885			0.256352
$93$	−5.97714	+	1.60157i	−0.619800	+	0.166075i
$94$			0.220025i			0.0226939i
$95$	−13.2610	+	7.65623i	−1.36055	+	0.785513i
$96$	−0.965926	−	0.258819i	−0.0985844	−	0.0264156i
$97$	1.25085	+	4.66823i	0.127004	+	0.473987i	0.999903	−	0.0139144i	$-0.00442922\pi$
$97$	1.25085	+	4.66823i	0.127004	+	0.473987i	−0.872899	+	0.487901i	$0.837763\pi$
$98$	1.22507	+	6.89197i	0.123751	+	0.696194i
$99$	1.45718	−	1.45718i	0.146452	−	0.146452i
$100$	0.710261			0.0710261
$101$	−17.9123			−1.78234			−0.891168	−	0.453674i	$-0.850113\pi$
$101$	−17.9123			−1.78234			−0.891168	+	0.453674i	$0.850113\pi$
$102$	−1.95091	+	1.95091i	−0.193169	+	0.193169i
$103$	6.30284	+	10.9168i	0.621038	+	1.07567i	0.989293	+	0.145944i	$0.0466219\pi$
$103$	6.30284	+	10.9168i	0.621038	+	1.07567i	−0.368255	+	0.929725i	$0.620045\pi$
$104$	2.58952	−	2.50887i	0.253923	−	0.246014i
$105$	5.60595	−	2.92320i	0.547085	−	0.285276i
$106$	1.96741	−	7.34246i	0.191091	−	0.713162i
$107$	−1.77111	+	3.06765i	−0.171220	+	0.296561i	−0.938847	−	0.344336i	$-0.888104\pi$
$107$	−1.77111	+	3.06765i	−0.171220	+	0.296561i	0.767627	+	0.640897i	$0.221437\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	6.36732	−	1.70612i	0.609879	−	0.163417i	0.0593564	−	0.998237i	$-0.481095\pi$
$109$	6.36732	−	1.70612i	0.609879	−	0.163417i	0.550523	+	0.834820i	$0.314428\pi$
$110$	−3.48210	+	3.48210i	−0.332005	+	0.332005i
$111$	−10.4827	+	2.80883i	−0.994975	+	0.266603i
$112$	2.58264	−	0.574432i	0.244037	−	0.0542787i
$113$	9.45257	−	16.3723i	0.889223	−	1.54018i	0.0484276	−	0.998827i	$-0.484579\pi$
$113$	9.45257	−	16.3723i	0.889223	−	1.54018i	0.840795	−	0.541353i	$-0.182088\pi$
$114$	5.54942	+	3.20396i	0.519751	+	0.300078i
$115$	4.15474	+	4.15474i	0.387432	+	0.387432i
$116$	−2.93821	−	1.69638i	−0.272806	−	0.157504i
$117$	−3.60510	−	0.0570287i	−0.333292	−	0.00527231i
$118$		−	9.61828i		−	0.885435i
$119$	2.19023	−	6.96332i	0.200778	−	0.638326i
$120$	−1.19481	−	2.06947i	−0.109071	−	0.188916i
$121$			6.75326i			0.613933i
$122$	2.30899	+	8.61725i	0.209046	+	0.780169i
$123$	−2.65770	+	9.91867i	−0.239637	+	0.894336i
$124$	−4.37557	−	4.37557i	−0.392938	−	0.392938i
$125$	−7.24843	−	7.24843i	−0.648319	−	0.648319i
$126$	−2.23239	−	1.42002i	−0.198877	−	0.126505i
$127$	0.650913	−	0.375805i	0.0577592	−	0.0333473i	−0.470842	−	0.882217i	$-0.656050\pi$
$127$	0.650913	−	0.375805i	0.0577592	−	0.0333473i	0.528602	+	0.848870i	$0.322717\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	3.95373	−	6.84806i	0.348106	−	0.602938i
$130$	8.61480	+	0.136277i	0.755568	+	0.0119523i
$131$	−6.09385	+	3.51829i	−0.532422	+	0.307394i	−0.742002	−	0.670397i	$-0.766124\pi$
$131$	−6.09385	+	3.51829i	−0.532422	+	0.307394i	0.209580	+	0.977791i	$0.432790\pi$
$132$	1.99054	+	0.533364i	0.173254	+	0.0464234i
$133$	−16.9381	−	0.727796i	−1.46872	−	0.0631079i
$134$	5.60896	+	3.23834i	0.484541	+	0.279750i
$135$	−0.618478	+	2.30819i	−0.0532301	+	0.198657i
$136$	−2.66500	−	0.714084i	−0.228522	−	0.0612322i
$137$	11.7374	+	3.14501i	1.00279	+	0.268697i	0.722614	−	0.691252i	$-0.242941\pi$
$137$	11.7374	+	3.14501i	1.00279	+	0.268697i	0.280176	+	0.959949i	$0.409607\pi$
$138$	0.636396	−	2.37506i	0.0541736	−	0.202179i
$139$	−1.67207	−	0.965371i	−0.141823	−	0.0818817i	0.427409	−	0.904058i	$-0.359426\pi$
$139$	−1.67207	−	0.965371i	−0.141823	−	0.0818817i	−0.569233	+	0.822176i	$0.692760\pi$
$140$	5.33455	+	3.39329i	0.450851	+	0.286786i
$141$	0.212528	+	0.0569467i	0.0178981	+	0.00479578i
$142$	−5.10738	+	2.94875i	−0.428602	+	0.247453i
$143$	−5.33638	+	5.17017i	−0.446250	+	0.432352i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−2.09834	−	7.83112i	−0.174258	−	0.650339i
$146$	−10.5558	+	6.09438i	−0.873602	+	0.504374i
$147$	6.97420	+	0.600442i	0.575222	+	0.0495236i
$148$	−7.67387	−	7.67387i	−0.630789	−	0.630789i
$149$	−2.32935	−	2.32935i	−0.190828	−	0.190828i	0.605226	−	0.796054i	$-0.293083\pi$
$149$	−2.32935	−	2.32935i	−0.190828	−	0.190828i	−0.796054	+	0.605226i	$0.793083\pi$
$150$	0.183829	−	0.686059i	0.0150096	−	0.0560165i
$151$	−2.01279	−	7.51183i	−0.163798	−	0.611304i	−0.998190	−	0.0601327i	$-0.980848\pi$
$151$	−2.01279	−	7.51183i	−0.163798	−	0.611304i	0.834392	−	0.551172i	$-0.185819\pi$
$152$			6.40792i			0.519751i
$153$	1.37950	+	2.38937i	0.111526	+	0.193169i
$154$	−5.32220	+	1.18377i	−0.428875	+	0.0953907i
$155$		−	14.7869i		−	1.18771i
$156$	−1.75316	−	3.15062i	−0.140365	−	0.252252i
$157$	10.5264	+	6.07743i	0.840099	+	0.485031i	0.857298	−	0.514821i	$-0.172142\pi$
$157$	10.5264	+	6.07743i	0.840099	+	0.485031i	−0.0171989	+	0.999852i	$0.505475\pi$
$158$	5.37338	+	5.37338i	0.427483	+	0.427483i
$159$	−6.58307	−	3.80074i	−0.522071	−	0.301418i
$160$	1.19481	−	2.06947i	0.0944578	−	0.163606i
$161$	1.41244	+	6.35031i	0.111316	+	0.500475i
$162$	0.965926	−	0.258819i	0.0758903	−	0.0203347i
$163$	−6.45477	+	6.45477i	−0.505576	+	0.505576i	−0.913165	−	0.407589i	$-0.866370\pi$
$163$	−6.45477	+	6.45477i	−0.505576	+	0.505576i	0.407589	+	0.913165i	$0.366370\pi$
$164$	−9.91867	+	2.65770i	−0.774518	+	0.207531i
$165$	2.46221	+	4.26468i	0.191683	+	0.332005i
$166$	−6.49547	+	11.2505i	−0.504146	+	0.873207i
$167$	6.47072	−	24.1491i	0.500719	−	1.86871i	0.00542397	−	0.999985i	$-0.498273\pi$
$167$	6.47072	−	24.1491i	0.500719	−	1.86871i	0.495295	−	0.868725i	$-0.335060\pi$
$168$	0.113578	−	2.64331i	0.00876270	−	0.203936i
$169$	12.9935	+	0.411189i	0.999500	+	0.0316299i
$170$	−3.29649	−	5.70968i	−0.252829	−	0.437913i
$171$	4.53108	−	4.53108i	0.346501	−	0.346501i
$172$	7.90746			0.602938
$173$	7.96526			0.605588			0.302794	−	0.953056i	$-0.402081\pi$
$173$	7.96526			0.605588			0.302794	+	0.953056i	$0.402081\pi$
$174$	−2.39904	+	2.39904i	−0.181871	+	0.181871i
$175$	0.407997	+	1.83435i	0.0308416	+	0.138664i
$176$	0.533364	+	1.99054i	0.0402038	+	0.150043i
$177$	−9.29055	−	2.48940i	−0.698320	−	0.187114i
$178$	0.368429	−	0.212712i	0.0276149	−	0.0159435i
$179$			9.92819i			0.742068i	0.928619	+	0.371034i	$0.120997\pi$
$179$			9.92819i			0.742068i	−0.928619	+	0.371034i	$0.879003\pi$
$180$	−2.30819	+	0.618478i	−0.172042	+	0.0460986i
$181$	16.1564			1.20090			0.600449	−	0.799663i	$-0.294989\pi$
$181$	16.1564			1.20090			0.600449	+	0.799663i	$0.294989\pi$
$182$	7.96700	+	5.24661i	0.590553	+	0.388905i
$183$	8.92123			0.659477
$184$	2.37506	−	0.636396i	0.175092	−	0.0469157i
$185$		−	25.9333i		−	1.90665i
$186$	−5.35896	+	3.09399i	−0.392938	+	0.226863i
$187$	5.49193	+	1.47156i	0.401609	+	0.107611i
$188$	0.0569467	+	0.212528i	0.00415327	+	0.0155002i
$189$	−1.94942	+	1.78879i	−0.141799	+	0.130116i
$190$	−10.8275	+	10.8275i	−0.785513	+	0.785513i
$191$	8.41537			0.608915			0.304457	−	0.952526i	$-0.401525\pi$
$191$	8.41537			0.608915			0.304457	+	0.952526i	$0.401525\pi$
$192$	−1.00000			−0.0721688
$193$	1.98752	−	1.98752i	0.143065	−	0.143065i	−0.631947	−	0.775012i	$-0.717744\pi$
$193$	1.98752	−	1.98752i	0.143065	−	0.143065i	0.775012	+	0.631947i	$0.217744\pi$
$194$	2.41645	+	4.18542i	0.173491	+	0.300496i
$195$	2.36131	−	8.28599i	0.169097	−	0.593372i
$196$	2.96710	+	6.34006i	0.211936	+	0.452861i
$197$	0.411028	−	1.53398i	0.0292845	−	0.109291i	−0.949737	−	0.313050i	$-0.898649\pi$
$197$	0.411028	−	1.53398i	0.0292845	−	0.109291i	0.979021	+	0.203759i	$0.0653159\pi$
$198$	1.03038	−	1.78467i	0.0732260	−	0.126831i
$199$	9.14210	+	15.8346i	0.648066	+	1.12248i	0.983584	+	0.180450i	$0.0577554\pi$
$199$	9.14210	+	15.8346i	0.648066	+	1.12248i	−0.335518	+	0.942034i	$0.608911\pi$
$200$	0.686059	−	0.183829i	0.0485117	−	0.0129987i
$201$	4.57970	−	4.57970i	0.323027	−	0.323027i
$202$	−17.3019	+	4.63603i	−1.21736	+	0.326190i
$203$	2.69333	−	8.56278i	0.189034	−	0.600990i
$204$	−1.37950	+	2.38937i	−0.0965847	+	0.167290i
$205$	−21.2504	−	12.2690i	−1.48420	−	0.856901i
$206$	8.91357	+	8.91357i	0.621038	+	0.621038i
$207$	−2.12942	−	1.22942i	−0.148005	−	0.0854508i
$208$	1.85194	−	3.09359i	0.128409	−	0.214502i
$209$		−	13.2052i		−	0.913422i
$210$	4.65835	−	4.27453i	0.321457	−	0.294970i
$211$	−11.9533	−	20.7037i	−0.822897	−	1.42530i	−0.903516	−	0.428555i	$-0.859023\pi$
$211$	−11.9533	−	20.7037i	−0.822897	−	1.42530i	0.0806186	−	0.996745i	$-0.474310\pi$
$212$		−	7.60147i		−	0.522071i
$213$	1.52638	+	5.69654i	0.104586	+	0.390321i
$214$	−0.916795	+	3.42152i	−0.0626708	+	0.233891i
$215$	13.3613	+	13.3613i	0.911235	+	0.911235i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	8.78705	−	13.8140i	0.596504	−	0.937755i
$218$	5.70879	−	3.29597i	0.386648	−	0.223231i
$219$	3.15468	+	11.7734i	0.213174	+	0.795575i
$220$	−2.46221	+	4.26468i	−0.166002	+	0.287525i
$221$	−4.83699	−	8.69260i	−0.325371	−	0.584727i
$222$	−9.39854	+	5.42625i	−0.630789	+	0.364186i
$223$	−6.30179	−	1.68856i	−0.421999	−	0.113074i	0.0415691	−	0.999136i	$-0.486764\pi$
$223$	−6.30179	−	1.68856i	−0.421999	−	0.113074i	−0.463568	+	0.886061i	$0.653431\pi$
$224$	2.34596	−	1.22330i	0.156746	−	0.0817348i
$225$	−0.615104	−	0.355130i	−0.0410069	−	0.0236754i
$226$	4.89301	−	18.2610i	0.325478	−	1.21470i
$227$	−20.3270	−	5.44662i	−1.34915	−	0.361505i	−0.489331	−	0.872098i	$-0.662759\pi$
$227$	−20.3270	−	5.44662i	−1.34915	−	0.361505i	−0.859822	+	0.510593i	$0.829426\pi$
$228$	6.18957	+	1.65849i	0.409915	+	0.109836i
$229$	−1.80606	+	6.74030i	−0.119348	+	0.445412i	−0.999575	−	0.0291400i	$-0.990723\pi$
$229$	−1.80606	+	6.74030i	−0.119348	+	0.445412i	0.880228	+	0.474552i	$0.157390\pi$
$230$	5.08850	+	2.93785i	0.335526	+	0.193716i
$231$	−0.234056	+	5.44724i	−0.0153998	+	0.358402i
$232$	−3.27715	−	0.878108i	−0.215155	−	0.0576506i
$233$	0.629559	−	0.363476i	0.0412438	−	0.0238121i	−0.479236	−	0.877686i	$-0.659086\pi$
$233$	0.629559	−	0.363476i	0.0412438	−	0.0238121i	0.520480	+	0.853874i	$0.325753\pi$
$234$	−3.49702	+	0.877983i	−0.228607	+	0.0573955i
$235$	−0.262888	+	0.455335i	−0.0171489	+	0.0297028i
$236$	−2.48940	−	9.29055i	−0.162046	−	0.604763i
$237$	6.58102	−	3.79955i	0.427483	−	0.246808i
$238$	0.313362	−	7.29292i	0.0203122	−	0.472730i
$239$	13.3792	+	13.3792i	0.865426	+	0.865426i	0.991962	−	0.126536i	$-0.0403860\pi$
$239$	13.3792	+	13.3792i	0.865426	+	0.865426i	−0.126536	+	0.991962i	$0.540386\pi$
$240$	−1.68971	−	1.68971i	−0.109071	−	0.109071i
$241$	−3.96561	+	14.7999i	−0.255447	+	0.953343i	0.712394	+	0.701780i	$0.247611\pi$
$241$	−3.96561	+	14.7999i	−0.255447	+	0.953343i	−0.967841	+	0.251563i	$0.919056\pi$
$242$	1.74787	+	6.52315i	0.112358	+	0.419324i
$243$		−	1.00000i		−	0.0641500i
$244$	4.46062	+	7.72601i	0.285562	+	0.494607i
$245$	−5.69932	+	15.7264i	−0.364116	+	1.00472i
$246$			10.2686i			0.654699i
$247$	−16.5934	+	16.0766i	−1.05581	+	1.02293i
$248$	−5.35896	−	3.09399i	−0.340294	−	0.196469i
$249$	9.18598	+	9.18598i	0.582138	+	0.582138i
$250$	−8.87748	−	5.12541i	−0.561461	−	0.324160i
$251$	−4.40452	+	7.62885i	−0.278011	+	0.481529i	−0.970890	−	0.239525i	$-0.923008\pi$
$251$	−4.40452	+	7.62885i	−0.278011	+	0.481529i	0.692880	+	0.721053i	$0.256342\pi$
$252$	−2.52385	−	0.793847i	−0.158987	−	0.0500077i
$253$	−4.89444	+	1.31146i	−0.307711	+	0.0824508i
$254$	0.531469	−	0.531469i	0.0333473	−	0.0333473i
$255$	−6.36832	+	1.70639i	−0.398800	+	0.106858i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.48712	+	9.50397i	−0.342277	+	0.592842i	−0.984855	−	0.173379i	$-0.944532\pi$
$257$	−5.48712	+	9.50397i	−0.342277	+	0.592842i	0.642578	+	0.766220i	$0.277865\pi$
$258$	2.04660	−	7.63802i	0.127416	−	0.475522i
$259$	15.4107	−	24.2270i	0.957576	−	1.50539i
$260$	8.35653	−	2.09804i	0.518250	−	0.130115i
$261$	1.69638	+	2.93821i	0.105003	+	0.181871i
$262$	−4.97561	+	4.97561i	−0.307394	+	0.307394i
$263$	4.45342			0.274610			0.137305	−	0.990529i	$-0.456156\pi$
$263$	4.45342			0.274610			0.137305	+	0.990529i	$0.456156\pi$
$264$	2.06076			0.126831
$265$	12.8443	−	12.8443i	0.789019	−	0.789019i
$266$	−16.5493	+	3.68091i	−1.01471	+	0.225691i
$267$	−0.110108	−	0.410929i	−0.00673851	−	0.0251484i
$268$	6.25598	+	1.67629i	0.382145	+	0.102395i
$269$	16.6432	−	9.60893i	1.01475	−	0.585867i	0.102172	−	0.994767i	$-0.467421\pi$
$269$	16.6432	−	9.60893i	1.01475	−	0.585867i	0.912579	+	0.408900i	$0.134087\pi$
$270$			2.38962i			0.145427i
$271$	2.78741	−	0.746885i	0.169323	−	0.0453700i	−0.173161	−	0.984893i	$-0.555398\pi$
$271$	2.78741	−	0.746885i	0.169323	−	0.0453700i	0.342485	+	0.939523i	$0.388732\pi$
$272$	−2.75901			−0.167290
$273$	7.12985	−	6.33760i	0.431518	−	0.383569i
$274$	12.1514			0.734093
$275$	−1.41380	+	0.378828i	−0.0852556	+	0.0228442i
$276$		−	2.45885i		−	0.148005i
$277$	17.2460	−	9.95700i	1.03621	−	0.598258i	0.117455	−	0.993078i	$-0.462526\pi$
$277$	17.2460	−	9.95700i	1.03621	−	0.598258i	0.918759	+	0.394820i	$0.129193\pi$
$278$	−1.86495	−	0.499713i	−0.111853	−	0.0299708i
$279$	1.60157	+	5.97714i	0.0958835	+	0.357842i
$280$	6.03102	+	1.89699i	0.360423	+	0.113367i
$281$	−3.51651	+	3.51651i	−0.209777	+	0.209777i	−0.804173	−	0.594396i	$-0.797391\pi$
$281$	−3.51651	+	3.51651i	−0.209777	+	0.209777i	0.594396	+	0.804173i	$0.297391\pi$
$282$	0.220025			0.0131023
$283$	−4.24489			−0.252333			−0.126166	−	0.992009i	$-0.540267\pi$
$283$	−4.24489			−0.252333			−0.126166	+	0.992009i	$0.540267\pi$
$284$	−4.17016	+	4.17016i	−0.247453	+	0.247453i
$285$	7.65623	+	13.2610i	0.453516	+	0.785513i
$286$	−3.81640	+	6.37516i	−0.225669	+	0.376971i
$287$	−12.5615	−	24.0897i	−0.741480	−	1.42197i
$288$	−0.258819	+	0.965926i	−0.0152511	+	0.0569177i
$289$	4.69393	−	8.13013i	0.276114	−	0.478243i
$290$	−4.05368	−	7.02119i	−0.238041	−	0.412298i
$291$	4.66823	−	1.25085i	0.273657	−	0.0733261i
$292$	−8.61876	+	8.61876i	−0.504374	+	0.504374i
$293$	−0.719912	+	0.192900i	−0.0420577	+	0.0112693i	−0.279787	−	0.960062i	$-0.590264\pi$
$293$	−0.719912	+	0.192900i	−0.0420577	+	0.0112693i	0.237729	+	0.971332i	$0.423597\pi$
$294$	6.89197	−	1.22507i	0.401948	−	0.0714477i
$295$	11.4920	−	19.9047i	0.669090	−	1.15890i
$296$	−9.39854	−	5.42625i	−0.546279	−	0.315394i
$297$	−1.45718	−	1.45718i	−0.0845541	−	0.0845541i
$298$	−2.85286	−	1.64710i	−0.165262	−	0.0954139i
$299$	7.60667	+	4.55363i	0.439905	+	0.263343i
$300$		−	0.710261i		−	0.0410069i
$301$	4.54230	+	20.4221i	0.261814	+	1.17711i
$302$	−3.88841	−	6.73492i	−0.223753	−	0.387551i
$303$			17.9123i			1.02903i
$304$	1.65849	+	6.18957i	0.0951210	+	0.354996i
$305$	−5.51759	+	20.5919i	−0.315936	+	1.17909i
$306$	1.95091	+	1.95091i	0.111526	+	0.111526i
$307$	−16.0161	−	16.0161i	−0.914090	−	0.914090i	0.0825012	−	0.996591i	$-0.473709\pi$
$307$	−16.0161	−	16.0161i	−0.914090	−	0.914090i	−0.996591	+	0.0825012i	$0.973709\pi$
$308$	−4.83447	+	2.52092i	−0.275470	+	0.143643i
$309$	10.9168	−	6.30284i	0.621038	−	0.358556i
$310$	−3.82714	−	14.2831i	−0.217367	−	0.811223i
$311$	6.78914	−	11.7591i	0.384977	−	0.666800i	−0.606789	−	0.794863i	$-0.707543\pi$
$311$	6.78914	−	11.7591i	0.384977	−	0.666800i	0.991766	+	0.128063i	$0.0408760\pi$
$312$	−2.50887	−	2.58952i	−0.142037	−	0.146602i
$313$	10.2314	−	5.90708i	0.578311	−	0.333888i	−0.182151	−	0.983271i	$-0.558306\pi$
$313$	10.2314	−	5.90708i	0.578311	−	0.333888i	0.760462	+	0.649383i	$0.224973\pi$
$314$	11.7407	+	3.14591i	0.662565	+	0.177534i
$315$	−2.92320	−	5.60595i	−0.164704	−	0.315860i
$316$	6.58102	+	3.79955i	0.370211	+	0.213742i
$317$	−2.37898	+	8.87846i	−0.133617	+	0.498664i	−1.00000		0.000715814i	$-0.999772\pi$
$317$	−2.37898	+	8.87846i	−0.133617	+	0.498664i	0.866383	+	0.499380i	$0.166439\pi$
$318$	−7.34246	−	1.96741i	−0.411745	−	0.110327i
$319$	6.75341	+	1.80957i	0.378119	+	0.101317i
$320$	0.618478	−	2.30819i	0.0345740	−	0.129032i
$321$	3.06765	+	1.77111i	0.171220	+	0.0988538i
$322$	3.00789	+	5.76836i	0.167623	+	0.321458i
$323$	17.0771	+	4.57579i	0.950195	+	0.254604i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	2.19726	+	1.31536i	0.121882	+	0.0729630i
$326$	−4.56421	+	7.90544i	−0.252788	+	0.437842i
$327$	−1.70612	−	6.36732i	−0.0943486	−	0.352114i
$328$	−8.89283	+	5.13428i	−0.491025	+	0.283493i
$329$	−0.516172	+	0.269156i	−0.0284575	+	0.0148390i
$330$	3.48210	+	3.48210i	0.191683	+	0.191683i
$331$	−13.2466	−	13.2466i	−0.728099	−	0.728099i	0.242142	−	0.970241i	$-0.422150\pi$
$331$	−13.2466	−	13.2466i	−0.728099	−	0.728099i	−0.970241	+	0.242142i	$0.922150\pi$
$332$	−3.36230	+	12.5483i	−0.184530	+	0.688677i
$333$	2.80883	+	10.4827i	0.153923	+	0.574449i
$334$		−	25.0009i		−	1.36799i
$335$	7.73838	+	13.4033i	0.422793	+	0.732298i
$336$	−0.574432	−	2.58264i	−0.0313378	−	0.140895i
$337$			19.5869i			1.06696i	0.845811	+	0.533482i	$0.179117\pi$
$337$			19.5869i			1.06696i	−0.845811	+	0.533482i	$0.820883\pi$
$338$	12.6572	−	2.96579i	0.688460	−	0.161318i
$339$	−16.3723	−	9.45257i	−0.889223	−	0.513393i
$340$	−4.66193	−	4.66193i	−0.252829	−	0.252829i
$341$	11.0435	+	6.37598i	0.598041	+	0.345279i
$342$	3.20396	−	5.54942i	0.173250	−	0.300078i
$343$	−14.6697	+	11.3049i	−0.792088	+	0.610406i
$344$	7.63802	−	2.04660i	0.411814	−	0.110345i
$345$	4.15474	−	4.15474i	0.223684	−	0.223684i
$346$	7.69386	−	2.06156i	0.413624	−	0.110830i
$347$	−1.45811	−	2.52552i	−0.0782754	−	0.135577i	0.824231	−	0.566254i	$-0.191608\pi$
$347$	−1.45811	−	2.52552i	−0.0782754	−	0.135577i	−0.902506	+	0.430677i	$0.858275\pi$
$348$	−1.69638	+	2.93821i	−0.0909353	+	0.157504i
$349$	8.28298	−	30.9125i	0.443378	−	1.65471i	−0.276806	−	0.960926i	$-0.589276\pi$
$349$	8.28298	−	30.9125i	0.443378	−	1.65471i	0.720184	−	0.693783i	$-0.244057\pi$
$350$	0.868859	+	1.66625i	0.0464424	+	0.0890646i
$351$	−0.0570287	+	3.60510i	−0.00304397	+	0.192426i
$352$	1.03038	+	1.78467i	0.0549195	+	0.0951233i
$353$	14.1873	−	14.1873i	0.755114	−	0.755114i	−0.220315	−	0.975429i	$-0.570708\pi$
$353$	14.1873	−	14.1873i	0.755114	−	0.755114i	0.975429	+	0.220315i	$0.0707085\pi$
$354$	−9.61828			−0.511206
$355$	−14.0927			−0.747965
$356$	0.300821	−	0.300821i	0.0159435	−	0.0159435i
$357$	−6.96332	−	2.19023i	−0.368538	−	0.115919i
$358$	2.56960	+	9.58989i	0.135808	+	0.506842i
$359$	20.8452	+	5.58546i	1.10017	+	0.294789i	0.762833	−	0.646596i	$-0.223808\pi$
$359$	20.8452	+	5.58546i	1.10017	+	0.294789i	0.337335	+	0.941385i	$0.390474\pi$
$360$	−2.06947	+	1.19481i	−0.109071	+	0.0629719i
$361$		−	22.0614i		−	1.16113i
$362$	15.6059	−	4.18159i	0.820229	−	0.219780i
$363$	6.75326			0.354454
$364$	9.05345	+	3.00583i	0.474530	+	0.157548i
$365$	−29.1264			−1.52455
$366$	8.61725	−	2.30899i	0.450431	−	0.120693i
$367$		−	9.80687i		−	0.511914i	−0.966688	−	0.255957i	$-0.917609\pi$
$367$		−	9.80687i		−	0.511914i	0.966688	−	0.255957i	$-0.0823906\pi$
$368$	2.12942	−	1.22942i	0.111004	−	0.0640881i
$369$	9.91867	+	2.65770i	0.516345	+	0.138354i
$370$	−6.71203	−	25.0496i	−0.348942	−	1.30227i
$371$	19.6319	−	4.36653i	1.01924	−	0.226699i
$372$	−4.37557	+	4.37557i	−0.226863	+	0.226863i
$373$	33.0030			1.70883			0.854414	−	0.519593i	$-0.173916\pi$
$373$	33.0030			1.70883			0.854414	+	0.519593i	$0.173916\pi$
$374$	5.68566			0.293998
$375$	−7.24843	+	7.24843i	−0.374307	+	0.374307i
$376$	0.110013	+	0.190548i	0.00567347	+	0.00982674i
$377$	−5.94804	−	10.6893i	−0.306340	−	0.550526i
$378$	−1.42002	+	2.23239i	−0.0730378	+	0.114822i
$379$	3.27222	−	12.2121i	0.168083	−	0.627294i	−0.829544	−	0.558441i	$-0.811400\pi$
$379$	3.27222	−	12.2121i	0.168083	−	0.627294i	0.997627	−	0.0688524i	$-0.0219337\pi$
$380$	−7.65623	+	13.2610i	−0.392756	+	0.680274i
$381$	−0.375805	−	0.650913i	−0.0192531	−	0.0333473i
$382$	8.12862	−	2.17806i	0.415896	−	0.111439i
$383$	−21.4213	+	21.4213i	−1.09458	+	1.09458i	−0.0995468	+	0.995033i	$0.531739\pi$
$383$	−21.4213	+	21.4213i	−1.09458	+	1.09458i	−0.995033	+	0.0995468i	$0.968261\pi$
$384$	−0.965926	+	0.258819i	−0.0492922	+	0.0132078i
$385$	−12.4285	−	3.90924i	−0.633415	−	0.199233i
$386$	1.40539	−	2.43421i	0.0715326	−	0.123898i
$387$	−6.84806	−	3.95373i	−0.348106	−	0.200979i
$388$	3.41738	+	3.41738i	0.173491	+	0.173491i
$389$	−33.6892	−	19.4505i	−1.70811	−	0.986179i	−0.936898	−	0.349602i	$-0.886317\pi$
$389$	−33.6892	−	19.4505i	−1.70811	−	0.986179i	−0.771214	−	0.636576i	$-0.780350\pi$
$390$	0.136277	−	8.61480i	0.00690064	−	0.436227i
$391$		−	6.78398i		−	0.343081i
$392$	4.50693	+	5.35608i	0.227634	+	0.270523i
$393$	3.51829	+	6.09385i	0.177474	+	0.307394i
$394$		−	1.58809i		−	0.0800068i
$395$	4.69988	+	17.5402i	0.236477	+	0.882543i
$396$	0.533364	−	1.99054i	0.0268026	−	0.100029i
$397$	1.06428	+	1.06428i	0.0534145	+	0.0534145i	0.733309	−	0.679895i	$-0.237975\pi$
$397$	1.06428	+	1.06428i	0.0534145	+	0.0534145i	−0.679895	+	0.733309i	$0.737975\pi$
$398$	12.9289	+	12.9289i	0.648066	+	0.648066i
$399$	−0.727796	+	16.9381i	−0.0364354	+	0.847967i
$400$	0.615104	−	0.355130i	0.0307552	−	0.0177565i
$401$	−0.520662	−	1.94314i	−0.0260006	−	0.0970355i	0.951706	−	0.307010i	$-0.0993285\pi$
$401$	−0.520662	−	1.94314i	−0.0260006	−	0.0970355i	−0.977707	+	0.209975i	$0.932662\pi$
$402$	3.23834	−	5.60896i	0.161514	−	0.279750i
$403$	−5.43295	−	21.6395i	−0.270635	−	1.07794i
$404$	−15.5125	+	8.95613i	−0.771774	+	0.445584i
$405$	2.30819	+	0.618478i	0.114695	+	0.0307324i
$406$	0.385341	−	8.96810i	0.0191241	−	0.445079i
$407$	19.3681	+	11.1822i	0.960043	+	0.554281i
$408$	−0.714084	+	2.66500i	−0.0353524	+	0.131937i
$409$	32.6342	+	8.74430i	1.61366	+	0.432378i	0.949129	−	0.314887i	$-0.101966\pi$
$409$	32.6342	+	8.74430i	1.61366	+	0.432378i	0.664527	+	0.747264i	$0.268633\pi$
$410$	−23.7018	−	6.35088i	−1.17055	−	0.313647i
$411$	3.14501	−	11.7374i	0.155132	−	0.578961i
$412$	10.9168	+	6.30284i	0.537834	+	0.310519i
$413$	22.5642	−	11.7660i	1.11031	−	0.578967i
$414$	−2.37506	−	0.636396i	−0.116728	−	0.0312772i
$415$	−26.8843	+	15.5217i	−1.31970	+	0.761929i
$416$	0.988154	−	3.46750i	0.0484482	−	0.170008i
$417$	−0.965371	+	1.67207i	−0.0472744	+	0.0818817i
$418$	−3.41775	−	12.7552i	−0.167168	−	0.623879i
$419$	3.64345	−	2.10355i	0.177994	−	0.102765i	−0.408356	−	0.912823i	$-0.633898\pi$
$419$	3.64345	−	2.10355i	0.177994	−	0.102765i	0.586350	+	0.810058i	$0.300564\pi$
$420$	3.39329	−	5.33455i	0.165576	−	0.260299i
$421$	−25.0874	−	25.0874i	−1.22269	−	1.22269i	−0.966674	−	0.256012i	$-0.917591\pi$
$421$	−25.0874	−	25.0874i	−1.22269	−	1.22269i	−0.256012	−	0.966674i	$-0.582409\pi$
$422$	−16.9045	−	16.9045i	−0.822897	−	0.822897i
$423$	0.0569467	−	0.212528i	0.00276885	−	0.0103335i
$424$	−1.96741	−	7.34246i	−0.0955456	−	0.356581i
$425$		−	1.95962i		−	0.0950554i
$426$	2.94875	+	5.10738i	0.142867	+	0.247453i
$427$	−17.3912	+	15.9582i	−0.841619	+	0.772273i
$428$			3.54222i			0.171220i
$429$	5.17017	+	5.33638i	0.249618	+	0.257643i
$430$	16.3642	+	9.44789i	0.789153	+	0.455618i
$431$	8.14787	+	8.14787i	0.392469	+	0.392469i	0.875567	−	0.483097i	$-0.160488\pi$
$431$	8.14787	+	8.14787i	0.392469	+	0.392469i	−0.483097	+	0.875567i	$0.660488\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−5.79948	+	10.0450i	−0.278705	+	0.482732i	−0.971063	−	0.238822i	$-0.923239\pi$
$433$	−5.79948	+	10.0450i	−0.278705	+	0.482732i	0.692358	+	0.721554i	$0.256572\pi$
$434$	4.91232	−	15.6175i	0.235799	−	0.749666i
$435$	−7.83112	+	2.09834i	−0.375473	+	0.100608i
$436$	4.66120	−	4.66120i	0.223231	−	0.223231i
$437$	−15.2192	+	4.07797i	−0.728033	+	0.195076i
$438$	6.09438	+	10.5558i	0.291201	+	0.504374i
$439$	−2.57299	+	4.45655i	−0.122802	+	0.212700i	−0.920872	−	0.389866i	$-0.872521\pi$
$439$	−2.57299	+	4.45655i	−0.122802	+	0.212700i	0.798070	+	0.602565i	$0.205855\pi$
$440$	−1.27454	+	4.75663i	−0.0607611	+	0.226763i
$441$	0.600442	−	6.97420i	0.0285925	−	0.332105i
$442$	−6.92198	−	7.14450i	−0.329245	−	0.339829i
$443$	2.29670	+	3.97800i	0.109119	+	0.189000i	0.915414	−	0.402514i	$-0.131864\pi$
$443$	2.29670	+	3.97800i	0.109119	+	0.189000i	−0.806294	+	0.591515i	$0.798530\pi$
$444$	−7.67387	+	7.67387i	−0.364186	+	0.364186i
$445$	1.01660			0.0481916
$446$	−6.52409			−0.308925
$447$	−2.32935	+	2.32935i	−0.110174	+	0.110174i
$448$	1.94942	−	1.78879i	0.0921012	−	0.0845125i
$449$	8.40409	+	31.3645i	0.396614	+	1.48018i	0.819014	+	0.573773i	$0.194521\pi$
$449$	8.40409	+	31.3645i	0.396614	+	1.48018i	−0.422401	+	0.906409i	$0.638812\pi$
$450$	−0.686059	−	0.183829i	−0.0323411	−	0.00866578i
$451$	18.3260	−	10.5805i	0.862938	−	0.498217i
$452$		−	18.9051i		−	0.889223i
$453$	−7.51183	+	2.01279i	−0.352937	+	0.0945691i
$454$	−21.0441			−0.987649
$455$	10.2187	+	20.3767i	0.479062	+	0.955276i
$456$	6.40792			0.300078
$457$	−22.8430	+	6.12077i	−1.06855	+	0.286318i	−0.749898	−	0.661553i	$-0.769898\pi$
$457$	−22.8430	+	6.12077i	−1.06855	+	0.286318i	−0.318654	+	0.947871i	$0.603231\pi$
$458$			6.97808i			0.326064i
$459$	2.38937	−	1.37950i	0.111526	−	0.0643898i
$460$	5.67549	+	1.52074i	0.264621	+	0.0709049i
$461$	4.55171	+	16.9872i	0.211994	+	0.791174i	0.987203	+	0.159469i	$0.0509781\pi$
$461$	4.55171	+	16.9872i	0.211994	+	0.791174i	−0.775209	+	0.631705i	$0.782355\pi$
$462$	1.18377	+	5.32220i	0.0550738	+	0.247611i
$463$	−18.9697	+	18.9697i	−0.881599	+	0.881599i	−0.993697	−	0.112098i	$-0.964243\pi$
$463$	−18.9697	+	18.9697i	−0.881599	+	0.881599i	0.112098	+	0.993697i	$0.464243\pi$
$464$	−3.39275			−0.157504
$465$	−14.7869			−0.685727
$466$	0.514032	−	0.514032i	0.0238121	−	0.0238121i
$467$	11.8859	+	20.5870i	0.550016	+	0.952655i	0.998273	+	0.0587503i	$0.0187116\pi$
$467$	11.8859	+	20.5870i	0.550016	+	0.952655i	−0.448257	+	0.893905i	$0.647955\pi$
$468$	−3.15062	+	1.75316i	−0.145638	+	0.0810399i
$469$	−0.735605	+	17.1199i	−0.0339671	+	0.790522i
$470$	−0.136081	+	0.507860i	−0.00627694	+	0.0234259i
$471$	6.07743	−	10.5264i	0.280033	−	0.485031i
$472$	−4.80914	−	8.32968i	−0.221359	−	0.383405i
$473$	−15.7401	+	4.21756i	−0.723732	+	0.193923i
$474$	5.37338	−	5.37338i	0.246808	−	0.246808i
$475$	−4.39621	+	1.17796i	−0.201712	+	0.0540486i
$476$	−1.58486	−	7.12553i	−0.0726421	−	0.326598i
$477$	−3.80074	+	6.58307i	−0.174024	+	0.301418i
$478$	16.3861	+	9.46049i	0.749481	+	0.432713i
$479$	22.2510	+	22.2510i	1.01667	+	1.01667i	0.999859	+	0.0168149i	$0.00535261\pi$
$479$	22.2510	+	22.2510i	1.01667	+	1.01667i	0.0168149	+	0.999859i	$0.494647\pi$
$480$	−2.06947	−	1.19481i	−0.0944578	−	0.0545353i
$481$	−9.52831	−	37.9514i	−0.434454	−	1.73043i
$482$			15.3219i			0.697895i
$483$	6.35031	−	1.41244i	0.288949	−	0.0642682i
$484$	3.37663	+	5.84850i	0.153483	+	0.265841i
$485$			11.5488i			0.524404i
$486$	−0.258819	−	0.965926i	−0.0117403	−	0.0438153i
$487$	−3.73942	+	13.9557i	−0.169449	+	0.632393i	0.827981	+	0.560755i	$0.189489\pi$
$487$	−3.73942	+	13.9557i	−0.169449	+	0.632393i	−0.997431	+	0.0716377i	$0.977177\pi$
$488$	6.30826	+	6.30826i	0.285562	+	0.285562i
$489$	6.45477	+	6.45477i	0.291895	+	0.291895i
$490$	−1.43483	+	16.6657i	−0.0648188	+	0.752878i
$491$	7.08716	−	4.09177i	0.319839	−	0.184659i	−0.331482	−	0.943462i	$-0.607549\pi$
$491$	7.08716	−	4.09177i	0.319839	−	0.184659i	0.651321	+	0.758802i	$0.274215\pi$
$492$	2.65770	+	9.91867i	0.119818	+	0.447168i
$493$	−4.68032	+	8.10654i	−0.210791	+	0.365100i
$494$	−11.8671	+	19.8235i	−0.533925	+	0.891901i
$495$	4.26468	−	2.46221i	0.191683	−	0.110668i
$496$	−5.97714	−	1.60157i	−0.268381	−	0.0719126i
$497$	−13.1655	−	8.37455i	−0.590553	−	0.375650i
$498$	11.2505	+	6.49547i	0.504146	+	0.291069i
$499$	−0.259203	+	0.967357i	−0.0116035	+	0.0433048i	−0.971485	−	0.237102i	$-0.923803\pi$
$499$	−0.259203	+	0.967357i	−0.0116035	+	0.0433048i	0.959881	+	0.280406i	$0.0904692\pi$
$500$	−9.90154	−	2.65311i	−0.442810	−	0.118651i
$501$	−24.1491	−	6.47072i	−1.07890	−	0.289090i
$502$	−2.27995	+	8.50888i	−0.101759	+	0.379770i
$503$	−28.0143	−	16.1741i	−1.24910	−	0.721166i	−0.278167	−	0.960533i	$-0.589727\pi$
$503$	−28.0143	−	16.1741i	−1.24910	−	0.721166i	−0.970929	+	0.239366i	$0.923060\pi$
$504$	−2.64331	−	0.113578i	−0.117742	−	0.00505915i
$505$	−41.3449	−	11.0783i	−1.83982	−	0.492979i
$506$	−4.38823	+	2.53355i	−0.195081	+	0.112630i
$507$	0.411189	−	12.9935i	0.0182615	−	0.577061i
$508$	0.375805	−	0.650913i	0.0166737	−	0.0288796i
$509$	−3.99545	−	14.9112i	−0.177095	−	0.660929i	−0.996185	−	0.0872636i	$-0.972188\pi$
$509$	−3.99545	−	14.9112i	−0.177095	−	0.660929i	0.819090	−	0.573665i	$-0.194479\pi$
$510$	−5.70968	+	3.29649i	−0.252829	+	0.145971i
$511$	−27.2100	−	17.3083i	−1.20370	−	0.765672i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−4.53108	−	4.53108i	−0.200052	−	0.200052i
$514$	−2.84034	+	10.6003i	−0.125282	+	0.467559i
$515$	7.79634	+	29.0963i	0.343548	+	1.28214i
$516$		−	7.90746i		−	0.348106i
$517$	−0.226710	−	0.392673i	−0.00997069	−	0.0172697i
$518$	8.61522	−	27.3901i	0.378531	−	1.20345i
$519$		−	7.96526i		−	0.349636i
$520$	7.52878	−	4.18938i	0.330159	−	0.183717i
$521$	25.6792	+	14.8259i	1.12503	+	0.649534i	0.942679	−	0.333700i	$-0.108297\pi$
$521$	25.6792	+	14.8259i	1.12503	+	0.649534i	0.182346	+	0.983234i	$0.441631\pi$
$522$	2.39904	+	2.39904i	0.105003	+	0.105003i
$523$	−13.7991	−	7.96693i	−0.603393	−	0.348369i	0.166982	−	0.985960i	$-0.446598\pi$
$523$	−13.7991	−	7.96693i	−0.603393	−	0.348369i	−0.770375	+	0.637591i	$0.779931\pi$
$524$	−3.51829	+	6.09385i	−0.153697	+	0.266211i
$525$	1.83435	−	0.407997i	0.0800575	−	0.0178064i
$526$	4.30168	−	1.15263i	0.187562	−	0.0502571i
$527$	−12.0722	+	12.0722i	−0.525875	+	0.525875i
$528$	1.99054	−	0.533364i	0.0866272	−	0.0232117i
$529$	−8.47704	−	14.6827i	−0.368567	−	0.638377i
$530$	9.08229	−	15.7310i	0.394510	−	0.683311i
$531$	−2.48940	+	9.29055i	−0.108031	+	0.403175i
$532$	−15.0327	+	7.83878i	−0.651752	+	0.339854i
$533$	−35.6062	−	10.1469i	−1.54228	−	0.439512i
$534$	−0.212712	−	0.368429i	−0.00920497	−	0.0159435i
$535$	−5.98534	+	5.98534i	−0.258769	+	0.258769i
$536$	6.47667			0.279750
$537$	9.92819			0.428433
$538$	13.5891	−	13.5891i	0.585867	−	0.585867i
$539$	−9.28770	−	11.0376i	−0.400050	−	0.475423i
$540$	0.618478	+	2.30819i	0.0266151	+	0.0993287i
$541$	22.2973	+	5.97454i	0.958635	+	0.256865i	0.704022	−	0.710178i	$-0.251385\pi$
$541$	22.2973	+	5.97454i	0.958635	+	0.256865i	0.254612	+	0.967043i	$0.418052\pi$
$542$	2.49913	−	1.44287i	0.107347	−	0.0619766i
$543$		−	16.1564i		−	0.693339i
$544$	−2.66500	+	0.714084i	−0.114261	+	0.0306161i
$545$	15.7522			0.674750
$546$	5.24661	−	7.96700i	0.224534	−	0.340956i
$547$	−31.3622			−1.34095			−0.670476	−	0.741931i	$-0.733910\pi$
$547$	−31.3622			−1.34095			−0.670476	+	0.741931i	$0.733910\pi$
$548$	11.7374	−	3.14501i	0.501395	−	0.134348i
$549$		−	8.92123i		−	0.380749i
$550$	−1.26758	+	0.731839i	−0.0540499	+	0.0312057i
$551$	20.9997	+	5.62685i	0.894616	+	0.239712i
$552$	−0.636396	−	2.37506i	−0.0270868	−	0.101089i
$553$	−6.03253	+	19.1790i	−0.256529	+	0.815574i
$554$	14.0813	−	14.0813i	0.598258	−	0.598258i
$555$	−25.9333			−1.10081
$556$	−1.93074			−0.0818817
$557$	−11.8083	+	11.8083i	−0.500333	+	0.500333i	−0.911541	−	0.411208i	$-0.865107\pi$
$557$	−11.8083	+	11.8083i	−0.500333	+	0.500333i	0.411208	+	0.911541i	$0.365107\pi$
$558$	3.09399	+	5.35896i	0.130979	+	0.226863i
$559$	24.4625	+	14.6441i	1.03465	+	0.619380i
$560$	6.31650	+	0.271407i	0.266921	+	0.0114690i
$561$	1.47156	−	5.49193i	0.0621292	−	0.231869i
$562$	−2.48655	+	4.30683i	−0.104889	+	0.181672i
$563$	−11.3974	−	19.7409i	−0.480345	−	0.831981i	0.519401	−	0.854531i	$-0.326155\pi$
$563$	−11.3974	−	19.7409i	−0.480345	−	0.831981i	−0.999746	+	0.0225494i	$0.992822\pi$
$564$	0.212528	−	0.0569467i	0.00894905	−	0.00239789i
$565$	31.9443	−	31.9443i	1.34391	−	1.34391i
$566$	−4.10025	+	1.09866i	−0.172346	+	0.0461801i
$567$	1.78879	+	1.94942i	0.0751222	+	0.0818678i
$568$	−2.94875	+	5.10738i	−0.123727	+	0.214301i
$569$	−13.3466	−	7.70565i	−0.559517	−	0.323037i	0.193434	−	0.981113i	$-0.438037\pi$
$569$	−13.3466	−	7.70565i	−0.559517	−	0.323037i	−0.752952	+	0.658076i	$0.771371\pi$
$570$	10.8275	+	10.8275i	0.453516	+	0.453516i
$571$	7.75405	+	4.47680i	0.324497	+	0.187348i	0.653395	−	0.757017i	$-0.273344\pi$
$571$	7.75405	+	4.47680i	0.324497	+	0.187348i	−0.328898	+	0.944365i	$0.606677\pi$
$572$	−2.03635	+	7.14569i	−0.0851441	+	0.298776i
$573$		−	8.41537i		−	0.351557i
$574$	−18.3683	−	20.0177i	−0.766679	−	0.835522i
$575$	0.873211	+	1.51245i	0.0364154	+	0.0630733i
$576$			1.00000i			0.0416667i
$577$	5.08679	+	18.9842i	0.211766	+	0.790321i	0.987280	+	0.158991i	$0.0508240\pi$
$577$	5.08679	+	18.9842i	0.211766	+	0.790321i	−0.775514	+	0.631330i	$0.782509\pi$
$578$	2.42976	−	9.06798i	0.101065	−	0.377178i
$579$	−1.98752	−	1.98752i	−0.0825987	−	0.0825987i
$580$	−5.73277	−	5.73277i	−0.238041	−	0.238041i
$581$	−34.3391	−	1.47548i	−1.42463	−	0.0612132i
$582$	4.18542	−	2.41645i	0.173491	−	0.100165i
$583$	4.05435	+	15.1311i	0.167914	+	0.626664i
$584$	−6.09438	+	10.5558i	−0.252187	+	0.436801i
$585$	−8.28599	−	2.36131i	−0.342583	−	0.0976281i
$586$	−0.645455	+	0.372654i	−0.0266635	+	0.0153942i
$587$	25.4182	+	6.81079i	1.04912	+	0.281111i	0.741889	−	0.670523i	$-0.233930\pi$
$587$	25.4182	+	6.81079i	1.04912	+	0.281111i	0.307233	+	0.951634i	$0.400597\pi$
$588$	6.34006	−	2.96710i	0.261459	−	0.122361i
$589$	34.3398	+	19.8261i	1.41494	+	0.816919i
$590$	5.94870	−	22.2008i	0.244904	−	0.913994i
$591$	−1.53398	−	0.411028i	−0.0630994	−	0.0169074i
$592$	−10.4827	−	2.80883i	−0.430837	−	0.115442i
$593$	−0.793101	+	2.95989i	−0.0325688	+	0.121548i	−0.980296	−	0.197532i	$-0.936707\pi$
$593$	−0.793101	+	2.95989i	−0.0325688	+	0.121548i	0.947728	+	0.319080i	$0.103374\pi$
$594$	−1.78467	−	1.03038i	−0.0732260	−	0.0422770i
$595$	9.36213	−	14.7181i	0.383810	−	0.603382i
$596$	−3.18195	−	0.852601i	−0.130338	−	0.0349239i
$597$	15.8346	−	9.14210i	0.648066	−	0.374161i
$598$	8.52605	+	2.42972i	0.348656	+	0.0993586i
$599$	−5.14389	+	8.90947i	−0.210173	+	0.364031i	−0.951769	−	0.306816i	$-0.900736\pi$
$599$	−5.14389	+	8.90947i	−0.210173	+	0.364031i	0.741595	+	0.670848i	$0.234070\pi$
$600$	−0.183829	−	0.686059i	−0.00750479	−	0.0280083i
$601$	−11.5044	+	6.64207i	−0.469274	+	0.270936i	−0.715936	−	0.698166i	$-0.754000\pi$
$601$	−11.5044	+	6.64207i	−0.469274	+	0.270936i	0.246662	+	0.969102i	$0.420666\pi$
$602$	9.67315	+	18.5506i	0.394248	+	0.756067i
$603$	−4.57970	−	4.57970i	−0.186500	−	0.186500i
$604$	−5.49904	−	5.49904i	−0.223753	−	0.223753i
$605$	−4.17674	+	15.5878i	−0.169809	+	0.633735i
$606$	4.63603	+	17.3019i	0.188326	+	0.702842i
$607$		−	3.09146i		−	0.125478i	−0.998030	−	0.0627392i	$-0.980016\pi$
$607$		−	3.09146i		−	0.125478i	0.998030	−	0.0627392i	$-0.0199836\pi$
$608$	3.20396	+	5.54942i	0.129938	+	0.225059i
$609$	−8.56278	−	2.69333i	−0.346982	−	0.109139i
$610$			21.3183i			0.863153i
$611$	−0.217419	+	0.762938i	−0.00879583	+	0.0308652i
$612$	2.38937	+	1.37950i	0.0965847	+	0.0557632i
$613$	6.75349	+	6.75349i	0.272771	+	0.272771i	0.830215	−	0.557444i	$-0.188218\pi$
$613$	6.75349	+	6.75349i	0.272771	+	0.272771i	−0.557444	+	0.830215i	$0.688218\pi$
$614$	−19.6157	−	11.3251i	−0.791625	−	0.457045i
$615$	−12.2690	+	21.2504i	−0.494732	+	0.856901i
$616$	−4.01728	+	3.68627i	−0.161861	+	0.148524i
$617$	−6.75925	+	1.81114i	−0.272117	+	0.0729136i	−0.392297	−	0.919839i	$-0.628320\pi$
$617$	−6.75925	+	1.81114i	−0.272117	+	0.0729136i	0.120180	+	0.992752i	$0.461653\pi$
$618$	8.91357	−	8.91357i	0.358556	−	0.358556i
$619$	−32.6928	+	8.76001i	−1.31404	+	0.352095i	−0.846740	−	0.532007i	$-0.821438\pi$
$619$	−32.6928	+	8.76001i	−1.31404	+	0.352095i	−0.467295	+	0.884101i	$0.654771\pi$
$620$	−7.39346	−	12.8058i	−0.296928	−	0.514295i
$621$	−1.22942	+	2.12942i	−0.0493350	+	0.0854508i
$622$	3.51432	−	13.1156i	0.140911	−	0.525888i
$623$	0.949713	+	0.604111i	0.0380495	+	0.0242032i
$624$	−3.09359	−	1.85194i	−0.123843	−	0.0741369i
$625$	−14.0234	−	24.2893i	−0.560937	−	0.971571i
$626$	8.35387	−	8.35387i	0.333888	−	0.333888i
$627$	−13.2052			−0.527365
$628$	12.1549			0.485031
$629$	−21.1723	+	21.1723i	−0.844195	+	0.844195i
$630$	−4.27453	−	4.65835i	−0.170301	−	0.185593i
$631$	−3.06673	−	11.4452i	−0.122085	−	0.455626i	0.877634	−	0.479331i	$-0.159120\pi$
$631$	−3.06673	−	11.4452i	−0.122085	−	0.455626i	−0.999719	+	0.0237048i	$0.992454\pi$
$632$	7.34018	+	1.96679i	0.291976	+	0.0782349i
$633$	−20.7037	+	11.9533i	−0.822897	+	0.475100i
$634$			9.19166i			0.365047i
$635$	1.73486	−	0.464854i	0.0688458	−	0.0184472i
$636$	−7.60147			−0.301418
$637$	−2.56238	+	25.1084i	−0.101525	+	0.994833i
$638$	6.99165			0.276802
$639$	5.69654	−	1.52638i	0.225352	−	0.0603828i
$640$		−	2.38962i		−	0.0944578i
$641$	−2.28521	+	1.31937i	−0.0902603	+	0.0521118i	−0.544451	−	0.838793i	$-0.683262\pi$
$641$	−2.28521	+	1.31937i	−0.0902603	+	0.0521118i	0.454190	+	0.890905i	$0.349929\pi$
$642$	3.42152	+	0.916795i	0.135037	+	0.0361830i
$643$	0.927043	+	3.45977i	0.0365590	+	0.136440i	0.981793	−	0.189953i	$-0.0608335\pi$
$643$	0.927043	+	3.45977i	0.0365590	+	0.136440i	−0.945234	+	0.326393i	$0.894167\pi$
$644$	4.39836	+	4.79331i	0.173320	+	0.188883i
$645$	13.3613	−	13.3613i	0.526102	−	0.526102i
$646$	17.6795			0.695591
$647$	−29.5283			−1.16088			−0.580439	−	0.814304i	$-0.697119\pi$
$647$	−29.5283			−1.16088			−0.580439	+	0.814304i	$0.697119\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	9.91049	+	17.1655i	0.389021	+	0.673804i
$650$	2.46283	+	0.701847i	0.0966001	+	0.0275287i
$651$	−13.8140	−	8.78705i	−0.541413	−	0.344392i
$652$	−2.36261	+	8.81738i	−0.0925269	+	0.345315i
$653$	16.7113	−	28.9449i	0.653966	−	1.13270i	−0.328186	−	0.944613i	$-0.606437\pi$
$653$	16.7113	−	28.9449i	0.653966	−	1.13270i	0.982152	−	0.188089i	$-0.0602292\pi$
$654$	−3.29597	−	5.70879i	−0.128883	−	0.223231i
$655$	−16.2418	+	4.35196i	−0.634618	+	0.170045i
$656$	−7.26097	+	7.26097i	−0.283493	+	0.283493i
$657$	11.7734	−	3.15468i	0.459326	−	0.123076i
$658$	−0.428921	+	0.393580i	−0.0167211	+	0.0153433i
$659$	4.47784	−	7.75585i	0.174432	−	0.302125i	−0.765533	−	0.643397i	$-0.777524\pi$
$659$	4.47784	−	7.75585i	0.174432	−	0.302125i	0.939965	+	0.341272i	$0.110858\pi$
$660$	4.26468	+	2.46221i	0.166002	+	0.0958415i
$661$	−20.5451	−	20.5451i	−0.799110	−	0.799110i	0.183845	−	0.982955i	$-0.441146\pi$
$661$	−20.5451	−	20.5451i	−0.799110	−	0.799110i	−0.982955	+	0.183845i	$0.941146\pi$
$662$	−16.2237	−	9.36676i	−0.630552	−	0.364049i
$663$	−8.69260	+	4.83699i	−0.337593	+	0.187853i
$664$			12.9909i			0.504146i
$665$	−38.6463	−	12.1558i	−1.49864	−	0.471380i
$666$	5.42625	+	9.39854i	0.210263	+	0.364186i
$667$		−	8.34225i		−	0.323013i
$668$	−6.47072	−	24.1491i	−0.250360	−	0.934355i
$669$	−1.68856	+	6.30179i	−0.0652834	+	0.243641i
$670$	10.9437	+	10.9437i	0.422793	+	0.422793i
$671$	−12.9998	−	12.9998i	−0.501853	−	0.501853i
$672$	−1.22330	−	2.34596i	−0.0471896	−	0.0904975i
$673$	−31.7291	+	18.3188i	−1.22307	+	0.706138i	−0.965571	−	0.260141i	$-0.916231\pi$
$673$	−31.7291	+	18.3188i	−1.22307	+	0.706138i	−0.257497	+	0.966279i	$0.582898\pi$
$674$	5.06945	+	18.9195i	0.195268	+	0.728750i
$675$	−0.355130	+	0.615104i	−0.0136690	+	0.0236754i
$676$	11.4583	−	6.14065i	0.440704	−	0.236179i
$677$	−14.0716	+	8.12424i	−0.540816	+	0.312240i	−0.745409	−	0.666607i	$-0.767746\pi$
$677$	−14.0716	+	8.12424i	−0.540816	+	0.312240i	0.204594	+	0.978847i	$0.434413\pi$
$678$	−18.2610	−	4.89301i	−0.701308	−	0.187915i
$679$	−6.86281	+	10.7889i	−0.263371	+	0.414041i
$680$	−5.70968	−	3.29649i	−0.218956	−	0.126414i
$681$	−5.44662	+	20.3270i	−0.208715	+	0.778934i
$682$	12.3175	+	3.30045i	0.471660	+	0.126381i
$683$	23.2320	+	6.22500i	0.888948	+	0.238193i	0.674264	−	0.738491i	$-0.264461\pi$
$683$	23.2320	+	6.22500i	0.888948	+	0.238193i	0.214684	+	0.976684i	$0.431128\pi$
$684$	1.65849	−	6.18957i	0.0634140	−	0.236664i
$685$	25.1469	+	14.5186i	0.960815	+	0.554727i
$686$	−11.2439	+	14.7165i	−0.429294	+	0.561878i
$687$	6.74030	+	1.80606i	0.257159	+	0.0689054i
$688$	6.84806	−	3.95373i	0.261080	−	0.150734i
$689$	14.0775	−	23.5159i	0.536308	−	0.895883i
$690$	2.93785	−	5.08850i	0.111842	−	0.193716i
$691$	11.5308	+	43.0337i	0.438654	+	1.63708i	0.732169	+	0.681123i	$0.238508\pi$
$691$	11.5308	+	43.0337i	0.438654	+	1.63708i	−0.293515	+	0.955954i	$0.594825\pi$
$692$	6.89812	−	3.98263i	0.262227	−	0.151397i
$693$	5.44724	+	0.234056i	0.206923	+	0.00889107i
$694$	−2.06208	−	2.06208i	−0.0782754	−	0.0782754i
$695$	−3.26240	−	3.26240i	−0.123750	−	0.123750i
$696$	−0.878108	+	3.27715i	−0.0332846	+	0.124220i
$697$	7.33262	+	27.3657i	0.277743	+	1.03655i
$698$		−	32.0030i		−	1.21133i
$699$	−0.363476	−	0.629559i	−0.0137479	−	0.0238121i
$700$	1.27051	+	1.38459i	0.0480207	+	0.0523327i
$701$			47.1989i			1.78268i	0.453336	+	0.891339i	$0.350234\pi$
$701$			47.1989i			1.78268i	−0.453336	+	0.891339i	$0.649766\pi$
$702$	0.877983	+	3.49702i	0.0331373	+	0.131986i
$703$	60.2251	+	34.7710i	2.27143	+	1.31141i
$704$	1.45718	+	1.45718i	0.0549195	+	0.0549195i
$705$	0.455335	+	0.262888i	0.0171489	+	0.00990093i
$706$	10.0319	−	17.3758i	0.377557	−	0.653948i
$707$	−32.0413	−	34.9184i	−1.20504	−	1.31324i
$708$	−9.29055	+	2.48940i	−0.349160	+	0.0935572i
$709$	35.0934	−	35.0934i	1.31796	−	1.31796i	0.402573	−	0.915388i	$-0.368116\pi$
$709$	35.0934	−	35.0934i	1.31796	−	1.31796i	0.915388	−	0.402573i	$-0.131884\pi$
$710$	−13.6125	+	3.64747i	−0.510870	+	0.136887i
$711$	−3.79955	−	6.58102i	−0.142494	−	0.246808i
$712$	0.212712	−	0.368429i	0.00797174	−	0.0138075i
$713$	3.93801	−	14.6969i	0.147480	−	0.550402i
$714$	−7.29292	−	0.313362i	−0.272931	−	0.0117273i
$715$	−15.5150	+	8.63332i	−0.580229	+	0.322868i
$716$	4.96409	+	8.59806i	0.185517	+	0.321325i
$717$	13.3792	−	13.3792i	0.499654	−	0.499654i
$718$	21.5805			0.805379
$719$	35.9725			1.34155			0.670774	−	0.741662i	$-0.265962\pi$
$719$	35.9725			1.34155			0.670774	+	0.741662i	$0.265962\pi$
$720$	−1.68971	+	1.68971i	−0.0629719	+	0.0629719i
$721$	−10.0070	+	31.8148i	−0.372680	+	1.18485i
$722$	−5.70992	−	21.3097i	−0.212501	−	0.793065i
$723$	14.7999	+	3.96561i	0.550413	+	0.147483i
$724$	13.9919	−	8.07822i	0.520004	−	0.300225i
$725$		−	2.40974i		−	0.0894954i
$726$	6.52315	−	1.74787i	0.242097	−	0.0648697i
$727$	8.17155			0.303066			0.151533	−	0.988452i	$-0.451579\pi$
$727$	8.17155			0.303066			0.151533	+	0.988452i	$0.451579\pi$
$728$	9.52293	+	0.560204i	0.352943	+	0.0207625i
$729$	−1.00000			−0.0370370
$730$	−28.1340	+	7.53848i	−1.04129	+	0.279012i
$731$		−	21.8168i		−	0.806922i
$732$	7.72601	−	4.46062i	0.285562	−	0.164869i
$733$	−6.62315	−	1.77467i	−0.244632	−	0.0655488i	0.134420	−	0.990924i	$-0.457083\pi$
$733$	−6.62315	−	1.77467i	−0.244632	−	0.0655488i	−0.379051	+	0.925376i	$0.623750\pi$
$734$	−2.53820	−	9.47271i	−0.0936868	−	0.349644i
$735$	15.7264	+	5.69932i	0.580078	+	0.210223i
$736$	1.73867	−	1.73867i	0.0640881	−	0.0640881i
$737$	−13.3469			−0.491638
$738$	10.2686			0.377991
$739$	35.6367	−	35.6367i	1.31092	−	1.31092i	0.390178	−	0.920740i	$-0.372414\pi$
$739$	35.6367	−	35.6367i	1.31092	−	1.31092i	0.920740	−	0.390178i	$-0.127586\pi$
$740$	−12.9666	−	22.4589i	−0.476663	−	0.825605i
$741$	16.0766	+	16.5934i	0.590589	+	0.609574i
$742$	17.8328	−	9.29884i	0.654662	−	0.341371i
$743$	9.95543	−	37.1542i	0.365229	−	1.36305i	−0.501881	−	0.864937i	$-0.667358\pi$
$743$	9.95543	−	37.1542i	0.365229	−	1.36305i	0.867110	−	0.498117i	$-0.165975\pi$
$744$	−3.09399	+	5.35896i	−0.113431	+	0.196469i
$745$	−3.93593	−	6.81724i	−0.144201	−	0.249764i
$746$	31.8784	−	8.54179i	1.16715	−	0.312737i
$747$	9.18598	−	9.18598i	0.336098	−	0.336098i
$748$	5.49193	−	1.47156i	0.200805	−	0.0538055i
$749$	−9.14829	+	2.03477i	−0.334271	+	0.0743487i
$750$	−5.12541	+	8.87748i	−0.187154	+	0.324160i
$751$	3.35077	+	1.93457i	0.122271	+	0.0705933i	0.559888	−	0.828568i	$-0.310844\pi$
$751$	3.35077	+	1.93457i	0.122271	+	0.0705933i	−0.437617	+	0.899161i	$0.644177\pi$
$752$	0.155581	+	0.155581i	0.00567347	+	0.00567347i
$753$	7.62885	+	4.40452i	0.278011	+	0.160510i
$754$	−8.51195	−	8.78558i	−0.309987	−	0.319952i
$755$		−	18.5836i		−	0.676327i
$756$	−0.793847	+	2.52385i	−0.0288719	+	0.0917914i
$757$	16.9076	+	29.2848i	0.614517	+	1.06437i	0.990469	+	0.137735i	$0.0439822\pi$
$757$	16.9076	+	29.2848i	0.614517	+	1.06437i	−0.375953	+	0.926639i	$0.622684\pi$
$758$		−	12.6429i		−	0.459211i
$759$	1.31146	+	4.89444i	0.0476030	+	0.177657i
$760$	−3.96316	+	14.7907i	−0.143759	+	0.536515i
$761$	−38.1244	−	38.1244i	−1.38201	−	1.38201i	−0.841046	−	0.540963i	$-0.818060\pi$
$761$	−38.1244	−	38.1244i	−1.38201	−	1.38201i	−0.540963	−	0.841046i	$-0.681940\pi$
$762$	−0.531469	−	0.531469i	−0.0192531	−	0.0192531i
$763$	14.7158	+	9.36067i	0.532746	+	0.338879i
$764$	7.28792	−	4.20768i	0.263668	−	0.152229i
$765$	1.70639	+	6.36832i	0.0616945	+	0.230247i
$766$	−15.1472	+	26.2357i	−0.547290	+	0.947934i
$767$	9.50435	−	33.3514i	0.343182	−	1.20425i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	23.8480	+	6.39007i	0.859983	+	0.230432i	0.661751	−	0.749724i	$-0.269814\pi$
$769$	23.8480	+	6.39007i	0.859983	+	0.230432i	0.198232	+	0.980155i	$0.436480\pi$
$770$	−13.0168	−	0.559305i	−0.469093	−	0.0201559i
$771$	9.50397	+	5.48712i	0.342277	+	0.197614i
$772$	0.727485	−	2.71501i	0.0261827	−	0.0977153i
$773$	30.5109	+	8.17538i	1.09740	+	0.294048i	0.761706	−	0.647922i	$-0.224362\pi$
$773$	30.5109	+	8.17538i	1.09740	+	0.294048i	0.335696	+	0.941970i	$0.391029\pi$
$774$	−7.63802	−	2.04660i	−0.274543	−	0.0735635i
$775$	1.13753	−	4.24533i	0.0408614	−	0.152497i
$776$	4.18542	+	2.41645i	0.150248	+	0.0867456i
$777$	−24.2270	−	15.4107i	−0.869138	−	0.552857i
$778$	−37.5755	−	10.0683i	−1.34715	−	0.360966i
$779$	56.9845	−	32.9000i	2.04168	−	1.17877i
$780$	−2.09804	−	8.35653i	−0.0751219	−	0.299212i
$781$	6.07667	−	10.5251i	0.217440	−	0.376617i
$782$	−1.75582	−	6.55282i	−0.0627881	−	0.234328i
$783$	2.93821	−	1.69638i	0.105003	−	0.0606235i
$784$	5.73961	+	4.00710i	0.204986	+	0.143111i
$785$	20.5382	+	20.5382i	0.733040	+	0.733040i
$786$	4.97561	+	4.97561i	0.177474	+	0.177474i
$787$	12.6003	−	47.0251i	0.449153	−	1.67626i	−0.255578	−	0.966788i	$-0.582266\pi$
$787$	12.6003	−	47.0251i	0.449153	−	1.67626i	0.704731	−	0.709474i	$-0.251068\pi$
$788$	−0.411028	−	1.53398i	−0.0146423	−	0.0546457i
$789$		−	4.45342i		−	0.158546i
$790$	9.07947	+	15.7261i	0.323033	+	0.559510i
$791$	48.8252	−	10.8597i	1.73602	−	0.386127i
$792$		−	2.06076i		−	0.0732260i
$793$	−0.508767	+	32.1619i	−0.0180668	+	1.14210i
$794$	1.30347	+	0.752557i	0.0462583	+	0.0267072i
$795$	−12.8443	−	12.8443i	−0.455541	−	0.455541i
$796$	15.8346	+	9.14210i	0.561242	+	0.324033i
$797$	−13.6108	+	23.5745i	−0.482118	+	0.835052i	−0.999789	−	0.0205271i	$-0.993466\pi$
$797$	−13.6108	+	23.5745i	−0.482118	+	0.835052i	0.517672	+	0.855579i	$0.326799\pi$
$798$	3.68091	+	16.5493i	0.130303	+	0.585840i
$799$	0.586367	−	0.157117i	0.0207442	−	0.00555839i
$800$	0.502230	−	0.502230i	0.0177565	−	0.0177565i
$801$	−0.410929	+	0.110108i	−0.0145195	+	0.00389048i
$802$	−1.00584	−	1.74217i	−0.0355175	−	0.0615181i
$803$	12.5591	−	21.7529i	0.443200	−	0.767644i
$804$	1.67629	−	6.25598i	0.0591180	−	0.220632i
$805$	−0.667347	+	15.5313i	−0.0235209	+	0.547406i
$806$	−10.8485	−	19.4960i	−0.382124	−	0.686718i
$807$	−9.60893	−	16.6432i	−0.338251	−	0.585867i
$808$	−12.6659	+	12.6659i	−0.445584	+	0.445584i
$809$	34.2916			1.20563			0.602814	−	0.797881i	$-0.294046\pi$
$809$	34.2916			1.20563			0.602814	+	0.797881i	$0.294046\pi$
$810$	2.38962			0.0839625
$811$	12.3600	−	12.3600i	0.434017	−	0.434017i	−0.455975	−	0.889993i	$-0.650709\pi$
$811$	12.3600	−	12.3600i	0.434017	−	0.434017i	0.889993	+	0.455975i	$0.150709\pi$
$812$	−1.94890	−	8.76225i	−0.0683931	−	0.307495i
$813$	−0.746885	−	2.78741i	−0.0261944	−	0.0977588i
$814$	21.6024	+	5.78833i	0.757162	+	0.202881i
$815$	−18.8910	+	10.9067i	−0.661722	+	0.382045i
$816$			2.75901i			0.0965847i
$817$	−48.9438	+	13.1144i	−1.71233	+	0.458817i
$818$	33.7854			1.18128
$819$	−6.33760	−	7.12985i	−0.221454	−	0.249137i
$820$	−24.5379			−0.856901
$821$	−38.3437	+	10.2742i	−1.33821	+	0.358571i	−0.855768	−	0.517359i	$-0.826915\pi$
$821$	−38.3437	+	10.2742i	−1.33821	+	0.358571i	−0.482438	+	0.875930i	$0.660248\pi$
$822$		−	12.1514i		−	0.423829i
$823$	26.4988	−	15.2991i	0.923692	−	0.533294i	0.0388808	−	0.999244i	$-0.487621\pi$
$823$	26.4988	−	15.2991i	0.923692	−	0.533294i	0.884811	+	0.465950i	$0.154287\pi$
$824$	12.1762	+	3.26259i	0.424177	+	0.113658i
$825$	0.378828	+	1.41380i	0.0131891	+	0.0492224i
$826$	18.7500	−	17.2051i	0.652397	−	0.598643i
$827$	−27.8201	+	27.8201i	−0.967399	+	0.967399i	−0.999485	−	0.0320857i	$-0.989785\pi$
$827$	−27.8201	+	27.8201i	−0.967399	+	0.967399i	0.0320857	+	0.999485i	$0.489785\pi$
$828$	−2.45885			−0.0854508
$829$	5.15948			0.179196			0.0895981	−	0.995978i	$-0.471442\pi$
$829$	5.15948			0.179196			0.0895981	+	0.995978i	$0.471442\pi$
$830$	−21.9510	+	21.9510i	−0.761929	+	0.761929i
$831$	−9.95700	−	17.2460i	−0.345405	−	0.598258i
$832$	0.0570287	−	3.60510i	0.00197712	−	0.124984i
$833$	17.4923	−	8.18626i	0.606071	−	0.283637i
$834$	−0.499713	+	1.86495i	−0.0173036	+	0.0645781i
$835$	29.8713	−	51.7386i	1.03374	−	1.79049i
$836$	−6.60260	−	11.4360i	−0.228356	−	0.395523i
$837$	5.97714	−	1.60157i	0.206600	−	0.0553583i
$838$	2.97486	−	2.97486i	0.102765	−	0.102765i
$839$	12.9421	−	3.46784i	0.446813	−	0.119723i	−0.0283950	−	0.999597i	$-0.509040\pi$
$839$	12.9421	−	3.46784i	0.446813	−	0.119723i	0.475208	+	0.879874i	$0.342373\pi$
$840$	1.89699	−	6.03102i	0.0654523	−	0.208090i
$841$	8.74462	−	15.1461i	0.301539	−	0.522280i
$842$	−30.7257	−	17.7395i	−1.05888	−	0.611343i
$843$	3.51651	+	3.51651i	0.121115	+	0.121115i
$844$	−20.7037	−	11.9533i	−0.712650	−	0.411449i
$845$	29.7372	+	8.98529i	1.02299	+	0.309103i
$846$		−	0.220025i		−	0.00756463i
$847$	−13.1649	+	12.0802i	−0.452352	+	0.415080i
$848$	−3.80074	−	6.58307i	−0.130518	−	0.226063i
$849$			4.24489i			0.145684i
$850$	−0.507186	−	1.89284i	−0.0173963	−	0.0649240i
$851$	6.90649	−	25.7754i	0.236751	−	0.883568i
$852$	4.17016	+	4.17016i	0.142867	+	0.142867i
$853$	29.2339	+	29.2339i	1.00095	+	1.00095i	1.00000		0.000949046i	$0.000302091\pi$
$853$	29.2339	+	29.2339i	1.00095	+	1.00095i	0.000949046		1.00000i	$0.499698\pi$
$854$	−12.6683	+	19.9156i	−0.433500	+	0.681499i
$855$	13.2610	−	7.65623i	0.453516	−	0.261838i
$856$	0.916795	+	3.42152i	0.0313354	+	0.116945i
$857$	17.1076	−	29.6313i	0.584385	−	1.01218i	−0.410567	−	0.911830i	$-0.634669\pi$
$857$	17.1076	−	29.6313i	0.584385	−	1.01218i	0.994952	−	0.100354i	$-0.0319975\pi$
$858$	6.37516	+	3.81640i	0.217644	+	0.130290i
$859$	−16.8204	+	9.71128i	−0.573906	+	0.331345i	−0.758708	−	0.651431i	$-0.774169\pi$
$859$	−16.8204	+	9.71128i	−0.573906	+	0.331345i	0.184802	+	0.982776i	$0.440836\pi$
$860$	18.2519	+	4.89059i	0.622385	+	0.166768i
$861$	−24.0897	+	12.5615i	−0.820974	+	0.428094i
$862$	9.97906	+	5.76141i	0.339888	+	0.196235i
$863$	−12.6379	+	47.1654i	−0.430200	+	1.60553i	0.322098	+	0.946706i	$0.395612\pi$
$863$	−12.6379	+	47.1654i	−0.430200	+	1.60553i	−0.752298	+	0.658823i	$0.771055\pi$
$864$	0.965926	+	0.258819i	0.0328615	+	0.00880520i
$865$	18.3854	+	4.92634i	0.625121	+	0.167501i
$866$	−3.00203	+	11.2037i	−0.102013	+	0.380719i
$867$	−8.13013	−	4.69393i	−0.276114	−	0.159414i
$868$	0.702817	−	16.3568i	0.0238552	−	0.555186i
$869$	−15.1263	−	4.05309i	−0.513126	−	0.137492i
$870$	−7.02119	+	4.05368i	−0.238041	+	0.137433i
$871$	16.2491	+	16.7714i	0.550580	+	0.568279i
$872$	3.29597	−	5.70879i	0.111616	−	0.193324i
$873$	−1.25085	−	4.66823i	−0.0423348	−	0.157996i
$874$	−13.6452	+	7.87804i	−0.461555	+	0.266479i
$875$	1.16426	−	27.0961i	0.0393593	−	0.916017i
$876$	8.61876	+	8.61876i	0.291201	+	0.291201i
$877$	16.2457	+	16.2457i	0.548578	+	0.548578i	0.926029	−	0.377451i	$-0.123199\pi$
$877$	16.2457	+	16.2457i	0.548578	+	0.548578i	−0.377451	+	0.926029i	$0.623199\pi$
$878$	−1.33188	+	4.97064i	−0.0449487	+	0.167751i
$879$	0.192900	+	0.719912i	0.00650635	+	0.0242820i
$880$			4.92443i			0.166002i
$881$	19.3700	+	33.5498i	0.652592	+	1.13032i	0.982492	+	0.186307i	$0.0596518\pi$
$881$	19.3700	+	33.5498i	0.652592	+	1.13032i	−0.329900	+	0.944016i	$0.607015\pi$
$882$	−1.22507	−	6.89197i	−0.0412504	−	0.232065i
$883$		−	34.0042i		−	1.14433i	−0.820138	−	0.572166i	$-0.806103\pi$
$883$		−	34.0042i		−	1.14433i	0.820138	−	0.572166i	$-0.193897\pi$
$884$	−8.53526	−	5.10952i	−0.287072	−	0.171852i
$885$	−19.9047	−	11.4920i	−0.669090	−	0.386299i
$886$	3.24802	+	3.24802i	0.109119	+	0.109119i
$887$	49.0966	+	28.3459i	1.64850	+	0.951763i	0.977668	+	0.210156i	$0.0673972\pi$
$887$	49.0966	+	28.3459i	1.64850	+	0.951763i	0.670834	+	0.741607i	$0.265936\pi$
$888$	−5.42625	+	9.39854i	−0.182093	+	0.315394i
$889$	1.89695	+	0.596663i	0.0636216	+	0.0200115i
$890$	0.981962	−	0.263116i	0.0329154	−	0.00881967i
$891$	−1.45718	+	1.45718i	−0.0488173	+	0.0488173i
$892$	−6.30179	+	1.68856i	−0.210999	+	0.0565371i
$893$	−0.704952	−	1.22101i	−0.0235903	−	0.0408596i
$894$	−1.64710	+	2.85286i	−0.0550872	+	0.0954139i
$895$	−6.14036	+	22.9162i	−0.205250	+	0.766003i
$896$	1.42002	−	2.23239i	0.0474394	−	0.0745788i
$897$	4.55363	−	7.60667i	0.152041	−	0.253979i
$898$	16.2355	+	28.1206i	0.541784	+	0.938398i
$899$	−14.8452	+	14.8452i	−0.495116	+	0.495116i
$900$	−0.710261			−0.0236754
$901$	−20.9725			−0.698696
$902$	14.9631	−	14.9631i	0.498217	−	0.498217i
$903$	20.4221	−	4.54230i	0.679605	−	0.151158i
$904$	−4.89301	−	18.2610i	−0.162739	−	0.607351i
$905$	37.2921	+	9.99240i	1.23963	+	0.332158i
$906$	−6.73492	+	3.88841i	−0.223753	+	0.129184i
$907$		−	34.0901i		−	1.13194i	−0.824425	−	0.565971i	$-0.808501\pi$
$907$		−	34.0901i		−	1.13194i	0.824425	−	0.565971i	$-0.191499\pi$
$908$	−20.3270	+	5.44662i	−0.674577	+	0.180752i
$909$	17.9123			0.594112
$910$	15.1444	+	17.0376i	0.502033	+	0.564791i
$911$	−25.9443			−0.859572			−0.429786	−	0.902931i	$-0.641411\pi$
$911$	−25.9443			−0.859572			−0.429786	+	0.902931i	$0.641411\pi$
$912$	6.18957	−	1.65849i	0.204957	−	0.0549181i
$913$		−	26.7712i		−	0.885999i
$914$	−20.4805	+	11.8244i	−0.677435	+	0.391117i
$915$	20.5919	+	5.51759i	0.680748	+	0.182406i
$916$	1.80606	+	6.74030i	0.0596739	+	0.222706i
$917$	−17.7592	−	5.58596i	−0.586462	−	0.184465i
$918$	1.95091	−	1.95091i	0.0643898	−	0.0643898i
$919$	−3.20533			−0.105734			−0.0528671	−	0.998602i	$-0.516836\pi$
$919$	−3.20533			−0.105734			−0.0528671	+	0.998602i	$0.516836\pi$
$920$	5.87569			0.193716
$921$	−16.0161	+	16.0161i	−0.527750	+	0.527750i
$922$	8.79323	+	15.2303i	0.289590	+	0.501584i
$923$	−20.6237	+	5.17790i	−0.678836	+	0.170433i
$924$	2.52092	+	4.83447i	0.0829322	+	0.159042i
$925$	1.99500	−	7.44546i	0.0655953	−	0.244805i
$926$	−13.4136	+	23.2331i	−0.440799	+	0.763487i
$927$	−6.30284	−	10.9168i	−0.207013	−	0.358556i
$928$	−3.27715	+	0.878108i	−0.107578	+	0.0288253i
$929$	21.9885	−	21.9885i	0.721420	−	0.721420i	−0.247474	−	0.968895i	$-0.579601\pi$
$929$	21.9885	−	21.9885i	0.721420	−	0.721420i	0.968895	+	0.247474i	$0.0796005\pi$
$930$	−14.2831	+	3.82714i	−0.468360	+	0.125497i
$931$	−28.8800	−	34.3213i	−0.946505	−	1.12484i
$932$	0.363476	−	0.629559i	0.0119060	−	0.0206219i
$933$	−11.7591	−	6.78914i	−0.384977	−	0.222267i
$934$	16.8093	+	16.8093i	0.550016	+	0.550016i
$935$	11.7663	+	6.79327i	0.384799	+	0.222164i
$936$	−2.58952	+	2.50887i	−0.0846410	+	0.0820048i
$937$			14.6025i			0.477044i	0.971137	+	0.238522i	$0.0766629\pi$
$937$			14.6025i			0.477044i	−0.971137	+	0.238522i	$0.923337\pi$
$938$	3.72041	+	16.7269i	0.121476	+	0.546153i
$939$	−5.90708	−	10.2314i	−0.192770	−	0.333888i
$940$			0.525776i			0.0171489i
$941$	4.61885	+	17.2378i	0.150570	+	0.561935i	0.999444	+	0.0333399i	$0.0106144\pi$
$941$	4.61885	+	17.2378i	0.150570	+	0.561935i	−0.848874	+	0.528595i	$0.822719\pi$
$942$	3.14591	−	11.7407i	0.102499	−	0.382532i
$943$	−17.8536	−	17.8536i	−0.581393	−	0.581393i
$944$	−6.80115	−	6.80115i	−0.221359	−	0.221359i
$945$	−5.60595	+	2.92320i	−0.182362	+	0.0950918i
$946$	−14.1122	+	8.14769i	−0.458828	+	0.264904i
$947$	−8.33131	−	31.0929i	−0.270731	−	1.01038i	−0.958648	−	0.284594i	$-0.908141\pi$
$947$	−8.33131	−	31.0929i	−0.270731	−	1.01038i	0.687917	−	0.725789i	$-0.258525\pi$
$948$	3.79955	−	6.58102i	0.123404	−	0.213742i
$949$	−42.6243	+	10.7015i	−1.38364	+	0.347386i
$950$	−3.94154	+	2.27565i	−0.127880	+	0.0738317i
$951$	8.87846	+	2.37898i	0.287904	+	0.0771436i
$952$	−3.37508	−	6.47254i	−0.109387	−	0.209776i
$953$	11.1576	+	6.44185i	0.361430	+	0.208672i	0.669708	−	0.742625i	$-0.266419\pi$
$953$	11.1576	+	6.44185i	0.361430	+	0.208672i	−0.308278	+	0.951296i	$0.599753\pi$
$954$	−1.96741	+	7.34246i	−0.0636971	+	0.237721i
$955$	19.4243	+	5.20472i	0.628555	+	0.168421i
$956$	18.2763	+	4.89711i	0.591097	+	0.158384i
$957$	1.80957	−	6.75341i	0.0584952	−	0.218307i
$958$	27.2518	+	15.7338i	0.880465	+	0.508337i
$959$	14.8647	+	28.5068i	0.480008	+	0.920531i
$960$	−2.30819	−	0.618478i	−0.0744965	−	0.0199613i
$961$	−6.31438	+	3.64561i	−0.203690	+	0.117600i
$962$	−19.0262	−	34.1921i	−0.613429	−	1.10240i
$963$	1.77111	−	3.06765i	0.0570733	−	0.0988538i
$964$	3.96561	+	14.7999i	0.127724	+	0.476671i
$965$	5.81683	−	3.35835i	0.187250	−	0.108109i
$966$	5.76836	−	3.00789i	0.185594	−	0.0967774i
$967$	−0.595818	−	0.595818i	−0.0191602	−	0.0191602i	0.697462	−	0.716622i	$-0.254313\pi$
$967$	−0.595818	−	0.595818i	−0.0191602	−	0.0191602i	−0.716622	+	0.697462i	$0.754313\pi$
$968$	4.77528	+	4.77528i	0.153483	+	0.153483i
$969$	4.57579	−	17.0771i	0.146996	−	0.548595i
$970$	2.98905	+	11.1553i	0.0959725	+	0.358174i
$971$		−	18.1225i		−	0.581578i	−0.956787	−	0.290789i	$-0.906082\pi$
$971$		−	18.1225i		−	0.581578i	0.956787	−	0.290789i	$-0.0939178\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−1.10908	−	4.98641i	−0.0355555	−	0.159857i
$974$			14.4480i			0.462944i
$975$	1.31536	−	2.19726i	0.0421252	−	0.0703686i
$976$	7.72601	+	4.46062i	0.247304	+	0.142781i
$977$	15.8175	+	15.8175i	0.506046	+	0.506046i	0.913310	−	0.407264i	$-0.133517\pi$
$977$	15.8175	+	15.8175i	0.506046	+	0.506046i	−0.407264	+	0.913310i	$0.633517\pi$
$978$	7.90544	+	4.56421i	0.252788	+	0.145947i
$979$	−0.438350	+	0.759244i	−0.0140097	+	0.0242655i
$980$	2.92745	+	16.4691i	0.0935141	+	0.526088i
$981$	−6.36732	+	1.70612i	−0.203293	+	0.0544722i
$982$	5.78664	−	5.78664i	0.184659	−	0.184659i
$983$	12.2775	−	3.28974i	0.391591	−	0.104926i	−0.0576507	−	0.998337i	$-0.518361\pi$
$983$	12.2775	−	3.28974i	0.391591	−	0.104926i	0.449241	+	0.893410i	$0.351694\pi$
$984$	5.13428	+	8.89283i	0.163675	+	0.283493i
$985$	1.89746	−	3.28650i	0.0604582	−	0.104717i
$986$	−2.42271	+	9.04167i	−0.0771548	+	0.287946i
$987$	0.269156	+	0.516172i	0.00856733	+	0.0164299i
$988$	−6.33201	+	22.2195i	−0.201448	+	0.706895i
$989$	9.72161	+	16.8383i	0.309129	+	0.535427i
$990$	3.48210	−	3.48210i	0.110668	−	0.110668i
$991$	43.8920			1.39428			0.697138	−	0.716937i	$-0.254457\pi$
$991$	43.8920			1.39428			0.697138	+	0.716937i	$0.254457\pi$
$992$	−6.18799			−0.196469
$993$	−13.2466	+	13.2466i	−0.420368	+	0.420368i
$994$	−14.8844	−	4.68171i	−0.472104	−	0.148495i
$995$	11.3084	+	42.2034i	0.358500	+	1.33794i
$996$	12.5483	+	3.36230i	0.397608	+	0.106539i
$997$	−38.8835	+	22.4494i	−1.23145	+	0.710980i	−0.967333	−	0.253510i	$-0.918415\pi$
$997$	−38.8835	+	22.4494i	−1.23145	+	0.710980i	−0.264121	+	0.964490i	$0.585082\pi$
$998$			1.00148i			0.0317013i
$999$	10.4827	−	2.80883i	0.331658	−	0.0888675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.a.115.8	yes	32
7.5	odd	6		546.2.cg.a.271.4	yes	32
13.6	odd	12		546.2.cg.a.409.4	yes	32
91.19	even	12	inner	546.2.by.a.19.8	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.a.19.8	✓	32	91.19	even	12	inner
546.2.by.a.115.8	yes	32	1.1	even	1	trivial
546.2.cg.a.271.4	yes	32	7.5	odd	6
546.2.cg.a.409.4	yes	32	13.6	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(2.30819 + 0.618478i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(1.78879 + 1.94942i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(2.30819 + 0.618478i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(1.78879 + 1.94942i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +2.38962 q^{10} +(-1.45718 + 1.45718i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(3.60510 + 0.0570287i) q^{13} +(2.23239 + 1.42002i) q^{14} +(0.618478 - 2.30819i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.37950 - 2.38937i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(-4.53108 + 4.53108i) q^{19} +(2.30819 - 0.618478i) q^{20} +(1.94942 - 1.78879i) q^{21} +(-1.03038 + 1.78467i) q^{22} +(2.12942 + 1.22942i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(0.615104 + 0.355130i) q^{25} +(3.49702 - 0.877983i) q^{26} +1.00000i q^{27} +(2.52385 + 0.793847i) q^{28} +(-1.69638 - 2.93821i) q^{29} -2.38962i q^{30} +(-1.60157 - 5.97714i) q^{31} +(0.258819 - 0.965926i) q^{32} +(1.45718 + 1.45718i) q^{33} +(-1.95091 - 1.95091i) q^{34} +(2.92320 + 5.60595i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-2.80883 - 10.4827i) q^{37} +(-3.20396 + 5.54942i) q^{38} +(0.0570287 - 3.60510i) q^{39} +(2.06947 - 1.19481i) q^{40} +(-9.91867 - 2.65770i) q^{41} +(1.42002 - 2.23239i) q^{42} +(6.84806 + 3.95373i) q^{43} +(-0.533364 + 1.99054i) q^{44} +(-2.30819 - 0.618478i) q^{45} +(2.37506 + 0.636396i) q^{46} +(-0.0569467 + 0.212528i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-0.600442 + 6.97420i) q^{49} +(0.686059 + 0.183829i) q^{50} +(-2.38937 + 1.37950i) q^{51} +(3.15062 - 1.75316i) q^{52} +(3.80074 - 6.58307i) q^{53} +(0.258819 + 0.965926i) q^{54} +(-4.26468 + 2.46221i) q^{55} +(2.64331 + 0.113578i) q^{56} +(4.53108 + 4.53108i) q^{57} +(-2.39904 - 2.39904i) q^{58} +(2.48940 - 9.29055i) q^{59} +(-0.618478 - 2.30819i) q^{60} +8.92123i q^{61} +(-3.09399 - 5.35896i) q^{62} +(-1.78879 - 1.94942i) q^{63} -1.00000i q^{64} +(8.28599 + 2.36131i) q^{65} +(1.78467 + 1.03038i) q^{66} +(4.57970 + 4.57970i) q^{67} +(-2.38937 - 1.37950i) q^{68} +(1.22942 - 2.12942i) q^{69} +(4.27453 + 4.65835i) q^{70} +(-5.69654 + 1.52638i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(-11.7734 + 3.15468i) q^{73} +(-5.42625 - 9.39854i) q^{74} +(0.355130 - 0.615104i) q^{75} +(-1.65849 + 6.18957i) q^{76} +(-5.44724 - 0.234056i) q^{77} +(-0.877983 - 3.49702i) q^{78} +(3.79955 + 6.58102i) q^{79} +(1.68971 - 1.68971i) q^{80} +1.00000 q^{81} -10.2686 q^{82} +(-9.18598 + 9.18598i) q^{83} +(0.793847 - 2.52385i) q^{84} +(-1.70639 - 6.36832i) q^{85} +(7.63802 + 2.04660i) q^{86} +(-2.93821 + 1.69638i) q^{87} +2.06076i q^{88} +(0.410929 - 0.110108i) q^{89} -2.38962 q^{90} +(6.33760 + 7.12985i) q^{91} +2.45885 q^{92} +(-5.97714 + 1.60157i) q^{93} +0.220025i q^{94} +(-13.2610 + 7.65623i) q^{95} +(-0.965926 - 0.258819i) q^{96} +(1.25085 + 4.66823i) q^{97} +(1.22507 + 6.89197i) q^{98} +(1.45718 - 1.45718i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{7} - 32 q^{9}+O(q^{10}) \) 32 * q + 8 * q^7 - 32 * q^9	\( 32 q + 8 q^{7} - 32 q^{9} - 4 q^{11} - 16 q^{12} + 4 q^{14} + 16 q^{16} - 8 q^{17} - 12 q^{19} - 8 q^{21} - 4 q^{22} - 24 q^{23} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 28 q^{31} + 4 q^{33} - 8 q^{34} - 44 q^{35} - 36 q^{37} + 8 q^{38} - 20 q^{39} - 28 q^{41} + 12 q^{42} + 84 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} + 24 q^{49} - 16 q^{50} + 8 q^{52} - 4 q^{53} + 48 q^{55} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 12 q^{59} - 40 q^{62} - 8 q^{63} - 4 q^{65} + 8 q^{67} - 8 q^{69} + 60 q^{70} + 20 q^{71} + 4 q^{73} + 20 q^{74} + 8 q^{75} + 36 q^{76} - 12 q^{77} - 20 q^{78} + 32 q^{81} - 48 q^{82} + 12 q^{83} - 16 q^{84} - 4 q^{85} + 52 q^{86} - 36 q^{87} - 36 q^{89} - 16 q^{92} + 4 q^{93} - 48 q^{95} + 76 q^{97} + 8 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q + 8 * q^7 - 32 * q^9 - 4 * q^11 - 16 * q^12 + 4 * q^14 + 16 * q^16 - 8 * q^17 - 12 * q^19 - 8 * q^21 - 4 * q^22 - 24 * q^23 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 28 * q^31 + 4 * q^33 - 8 * q^34 - 44 * q^35 - 36 * q^37 + 8 * q^38 - 20 * q^39 - 28 * q^41 + 12 * q^42 + 84 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 + 24 * q^49 - 16 * q^50 + 8 * q^52 - 4 * q^53 + 48 * q^55 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 12 * q^59 - 40 * q^62 - 8 * q^63 - 4 * q^65 + 8 * q^67 - 8 * q^69 + 60 * q^70 + 20 * q^71 + 4 * q^73 + 20 * q^74 + 8 * q^75 + 36 * q^76 - 12 * q^77 - 20 * q^78 + 32 * q^81 - 48 * q^82 + 12 * q^83 - 16 * q^84 - 4 * q^85 + 52 * q^86 - 36 * q^87 - 36 * q^89 - 16 * q^92 + 4 * q^93 - 48 * q^95 + 76 * q^97 + 8 * q^98 + 4 * q^99

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